Rate of change of r with respect to time is ((30t - 5t^2)(30 - 10t)) / sqrt((30t - 5t^2)^2 + d^2)
What is projectile?Projectile is an object that is propelled by the application of external force and then moves freely under the influence of gravity and air resistance.
Given, height of the rocket is, y = 30t - 5t^2, and distance between the observer and the rocket is r.
As, r = sqrt(d^2 + (y - 0)^2)
So, r = sqrt(d^2 + (30t - 5t^2 - 0)^2)
r = sqrt(d^2 + (30t - 5t^2)^2)
Then, dr/dt = (d^2 + (30t - 5t^2)^2)^(1/2) (2(30t - 5t^2)(-10t + 30)) / (2(d^2 + (30t - 5t^2)^2)^(1/2))
So, dr/dt = (30t - 5t^2)(30 - 10t) / sqrt((30t - 5t^2)^2 + d^2)
Therefore, rate of change of r with respect to time is ((30t - 5t^2)(30 - 10t)) / sqrt((30t - 5t^2)^2 + d^2).
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a comet that is moving southward from the north celestial pole toward the equator can be described as having its
A comet that is moving southward from north celestial pole towards equator can be described as having its declination decrease with time.
What do you understand by comets?Comets are frozen leftovers from the formation of solar system composed of dust, rock and ices. They range from few miles to tens of miles wide, but as they orbit closer to the Sun, they heat up and spew gases and dust into the glowing head that is larger than a planet.
Short-period comets takes less than 200 years whereas long-period comets take over 200 years with some taking 100,000 to 1 million years to orbit the Sun. Short-period comets are found near the ecliptic, which means they are orbiting the Sun in same plane as planets.
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A 5,824-kg railroad car moving at 4.5 m/s to the east collides with a 3,642-kg railroad car moving at 3.8 m/s to the west. If the cars couple together, what is their velocity after the collision?
The cars' post-collision velocity, if they were tied together, would be v = 1.30 m/s. We may use the Conservation of Momentum equation to determine the final velocity since we are dealing with two objects colliding.
When two objects collide, the left side of the equation represents the situation prior to the collision, and the right side of the equation represents the situation following the collision.
We are dealing with an inelastic collision if the automobiles are still connected after the accident.
Make the East the positive direction and the West the negative direction.
Car 1 will be the designation for the railroad car traveling east, while Car 2 will be the designation for the railroad car traveling west.
The following is a list of the factors we know based on the question itself:
m1 = 5824 kg, and m2 = 3642 kg.
4.5 m/s to the East for v1(i).
3.8 m/s to the West for v2(i).
Since the cars pair together after the impact, they will have the same ultimate velocity, which is what we are attempting to solve for.
Let's modify the Conservation of Momentum equation to include the known variables.
m₁v₁ + m₂v₂ = m₁v₁ + m₂v₂
(5824)(4.5) + (3642)(-3.8)
= (5824)(v) + (3642)(v1) (v2)
We can factor out "v" because the ultimate velocities for both cars are the same.
(5824)(4.5) + (3642)(-3.8) = (5824)(v) + (3642)(v)
Simplify the problem on both sides.
12368.4 = 9466 v
v = 1.30 m/s
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A 150 g ball is dropped from a height of 2.2 m , bounces on a hard floor, and rebounds to a height of 1.5 m . The figure(Figure 1) shows the impulse received from the floor. What maximum force does the floor exert on the ball? Express your answer to two significant figures and include the appropriate units. (5.0 ms as indicated by graph)
The maximum force in the floor exert on the ball is 60N.
What is maximum force?Maximum force is the amount of force that can be applied to an object before it breaks or fails. Maximum force is often referred to as the breaking strength or ultimate strength of an object. The maximum force can vary depending on the material, shape, size, and other factors. For example, the maximum force that a steel beam can withstand before failing may be much greater than the maximum force that a piece of paper can withstand. As such, the maximum force applied to an object must always be considered when designing, constructing, and using any material. Generally speaking, maximum force is measured in newtons or pounds, and is determined by various tests such as tension, compression, and shear tests. Ultimately, the maximum force that can be applied to an object is dependent on the material and its application, so it is important to be aware of the maximum force before using any material.Step 1: Calculate the change in momentum of the ball when it collides with the floor.
Step 2: Recall the impulse-momentum theorem, which states that the impulse imparted by an applied force is equal to the change in momentum of an object.
Step 3: Use the impulse-momentum theorem to calculate the force exerted by the floor on the ball.
Step 4: The force exerted by the floor on the ball can be calculated as follows:
Force = Impulse / Time = (150 g * (2.2 m - 1.5 m)) / (5.0 ms) = 60 N
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write down the equation for the gravitational potential energy of two particles of mass m and m seperated by a distance r.
The equation for the gravitational potential energy of two particles of mass m and m separated by a distance r −2G′m1m2/r
The energy that an item has or acquires when its location changes as a result of being in a gravitational field are known as gravitational potential energy. Gravitational potential energy can be defined as energy that has a connection to gravitational force or gravity.
The gravitational potential energy of this system is Gm1m2/r if m1 and m2 are two particles separated by a distance of r. we add the gravitational potential energies of the two particles with respect to one another and state that the system has (-2Gm1m2/r) like we do when we add the kinetic energy of the same system.
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based on the setup below, which of the following statements is true? (assume the car starts at rest and there is no friction.)
Despite touching the egg, the automobile won't crack it. The automobile cannot reach the egg because the egg on Hill 3 is higher than the starting height of the car on Hill 1.
What type of energy is present in the car when it is at the top of the ramp?The car's position at the top of the hill's potential energy is turning into kinetic energy as it descends. where "g," which is equal to 9.8 m/s2, is the gravitational constant.
What method may the student use to calculate the amount of mechanical energy lost through friction?The original spring potential energy held within the block-spring system is subtracted from the ultimate kinetic energy of the system.
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Answer:
The car will never reach the egg.
Explanation: Because the egg on Hill 3 is higher than the initial height of the car on Hill 1, the car will not be able to reach the egg. Unless it has some starting speed, the car will not be able to rise higher than its starting position.
As a result of an external interference, a voltage is induced in the signal S traveling on the PROFIBUS DP bus,
which increases the voltage pulse of the bits traveling in wires A and B by +0.5 V. How does the interference
appear in the voltage of the bits read by the receiver? Justify your answer.
The interference will cause the voltage of the bits read by the receiver to be shifted by +0.5V.
What is voltage?Generally, This is because the induced voltage will add to the original signal voltage, resulting in an overall increase in the voltage level of the bits traveling on wires A and B.
This shift in voltage can potentially cause errors in the signal being received, as the receiver may interpret the higher voltage levels as a different signal or data bit.
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5.19 block a in fig. 8.32 has mass 1,00 kg, and block bla, block a? b) how much potential energy was stored in the
When blocks are forced together, they compress a massless spring between them, storing 0.75 J of potential energy in the process.
What is potential energy?Potential energy in physics is the energy that an object retains as a result of its position in relation to other objects, internal stresses, electric charge, or other elements. Potential energy is a form of stored energy that is dependent on the relationship between different system components. When a spring is compressed or stretched, its potential energy increases.
Here,
let velocity of A be uf.
Maui+Mbvi=Mauf+Mbvb
0=1*uf+2*0.5
uf=-1 m/s
PE=ΔKE
=1/2*Ma*uf²+1/2*Mb*vf²
=1/2*1*1²+1/2*2*0.5²
PE=0.75 J
When blocks are forced together, a massless spring between them is compressed, storing 0.75 J of potential energy.
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complete question:
Block A in the figure has a mass of 1 kg and block B has a mass of 2 kg. The blocks are forced together compressing a mass-less spring between them and the system is released from rest on a level friction less surface. The spring is not fastened to either of the blocks, when spring regains its natural length, block B acquired a speed of 0.5 m/s. How much potential energy was stored in the compressed spring?
A jet of water squirts out horizontally from a hole near the bottom of the tank shown in Figure P14.84. If the hole has a diameter of 3.50 mm, what is the height h of the water level in the tank?
If the hole has a diameter of 3.50 mm, the height h of the water level in the tank is 9×10-2m.
Explain about Mechanical Properties of Fluids?
Mechanical properties of fluids are those properties that describe a fluid's behavior under a force or load. Examples of mechanical properties include viscosity, compressibility, surface tension and elasticity.
These properties are impacted by temperature, pressure and other external factors.Viscosity is a measure of a fluid's resistance to flow, compressibility is a measure of a fluid's ability to change its volume when pressure is applied, and surface tension is a measure of the attraction between particles of a substance.Elasticity is a measure of a fluid's ability to return to its original shape after being deformed.All of these properties are important in understanding the behavior of a fluid and how it will respond to various conditions.Step 1: Calculate the volume of water in the tank.
Volume = πr2h
where r is the radius of the tank and h is the height of the water level.
Step 2: Calculate the velocity of the jet of water.
Velocity = (2gh)1/2
where g is the acceleration due to gravity and h is the height of the water level.
Step 3: Calculate the mass flow rate of the jet of water.
Mass flow rate = ρAV
where ρ is the density of the water, A is the area of the hole and V is the velocity of the jet of water.
Step 4: Calculate the height h of the water level in the tank.
Height = (mass flow rate/πr2)1/2
where r is the radius of the hole.
Substituting the values,
h = 9×10-2m
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Determine the horizontal and vertical force components that the pins support at A and D exert on the four-member frame.
The given frame is determinant therefore it can be solved by the equilibrium equations .Therefore m+r-2j= 4+4-2*4=0 Therefore given given structure is determinant.
What is equilibrium equations?The static or dynamic equilibrium of all internal and external forces in the system is described by the equilibrium equation. When the resultant force and moment on each axis are equal to zero, a solid body is said to be in static equilibrium.
The equilibrium equations can be used to describe this. By calculating the resultant force and moment on each axis, we will demonstrate the equilibrium equations in this article. Gauss's theorem and Cauchy's formula can be used to arrive at a more sophisticated solution. International bibliography contains references to this strategy.
The given frame is determinant therefore it can be solved by the equilibrium equations,
For determinacy m+r-2j should be equal to zero
Here m =no. of members (4 in our case)
r = unknown reactions (4 in our case)
j= no. of joints (4 in our case)
Therefore m+r-2j= 4+4-2*4=0 Therefore given given structure is determinant.
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Complete question:
Determine the horizontal and vertical force components that the pins support at A and D exert on the four-member frame.
You wish to determine the height of the smokestack of a local coal burning power plant. You convince a member of the maintenance crew to mount the support for a simple pendulum at the top of the stack and you suspend a 1.00 kg mass that just misses the ground at its lowest point from the pendulum cord. If the period of the pendulum is 38.3 s, determine the height of the smokestack in m.
If you had the ability to take this pendulum to the moon, where the acceleration due to gravity is 1.67 m/s2, what would you expect the period of the pendulum to be in seconds.
Explanation:
To determine the height of the smokestack using a simple pendulum, we can use the formula:
T = 2π √(L/g)
where T is the period of the pendulum in seconds, L is the length of the pendulum in meters, and g is the acceleration due to gravity in m/s^2.
Given that the period of the pendulum is 38.3 s and the acceleration due to gravity on Earth is 9.8 m/s^2, we can solve for L:
38.3 = 2π √(L/9.8)
L = (38.3^2) * 9.8 / (4π^2)
L = (1461.69) / (39.4784)
L = 37.03 m
So the height of the smokestack is 37.03 m.
To find the period of the pendulum on the moon, we can use the same formula, but substitute the acceleration due to gravity on the moon, which is 1.67 m/s^2, for the value of g.
T = 2π √(L/1.67)
Given that L=37.03m, we can calculate the period of the pendulum on the moon:
T = 2π √(37.03/1.67)
T = 2π √22.24
T ≈ 45.5 seconds
(e) if a typical house uses 10,900kwh per year, calculate how many houses could have their full energy needs provided for one year by the turbine above if it continued to operate as described for one year. show your work.
50 housescould have their full energy needs provided for one year by the turbine above if it continued to operate as described for one year.
Describe energy physics.Energy is characterized as having the "ability to accomplish work, namely the capacity to apply a force sufficient to move an object." Despite this unclear definition, the concept is actually quite straightforward: energy is simply the force that moves objects.
1 week 10.5MWh
we know,
1 week = 7days.
Enregy produce per day
10.5
E
=
1-day
7
=1.5 MWh
also, 1 year = 365 days.
E1-year
Energy produce by turbine per year is:
= E × 365 days 1-day
=1.5 × 365
=547.5 MWh
E1-house
Energy consumption of 1- house per year:
= 10900 KWH
in MWh
10900
E
-MWh
1- house
103
= 10.9 MWh
Describe the energy formula.Albert Einstein created the equation E = mc2, which typically reads as follows: "When the power of a body functions by such an amount E (regardless of the form the power takes), its mass of the physical change by an equivalent amount to E/c2.
Total numbe of house =
Energy produce by turbine per year Energy consume by 1 houe per year
=
547.5
10.9
=50.229
= 50 houses (appromately)
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The correct question is
If a typical house uses 10,900 kWh per year, calculate how many houses could have their full energy needs provided for one year by the turbine above (the turbine above produces 10.5 MW per week) if it continued to operate as described for one year.
if a child of mass 40.2 kg sits in a seat, what is the tension in the chain (for the same angle)? answer in units of n.
The tension in the chain is the force acting on the child which is 394.76N.
What is tension the chain and calculate it?
The tension in the chain is equal to the force acting on the child in the seat. This force is equal to the child's weight, which is the force of gravity acting on the child's mass.
The weight of an object can be calculated using the formula:
Weight = mass x gravity
where mass is measured in kilograms and gravity is measured in meters per second squared. On Earth, the acceleration due to gravity is approximately 9.8 m/s^2.
So, for a child with a mass of 40.2 kg, the weight would be:
Weight = 40.2 kg x 9.8 m/s^2 = 394.76 N
The tension in the chain is the force acting on the child which is 394.76N. However, it's important to note that this tension is in the direction of the force of gravity, which is downwards.
If the angle of the chain is different from the vertical direction, the tension in the chain will be affected by the angle and the force of gravity.
In this case, you would need the angle to determine the tension in the chain.
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Position graph and time looking for velocity on runners for time interval between 5 seconds and 10 seconds
The Position-Time graph is the graph where the time t and the particle's instantaneous position x are shown on the y-axis and x-axis, respectively.
What is Position -Time Graph?A position-time graph, can be used to depict an object's motion. The y-axis of this sort of graph denotes position in relation to the starting point, while the x-axis denotes time. An object's distance from its beginning position at any given moment since it began moving is displayed on a position-time graph.
In a position-time graph, the slope, or steepness, of the graph line represents the velocity of the moving item. The slope and velocity are both zero if the graph line is horizontal. The object's position is staying the same. The greater the slope of the line and the faster the object's velocity changes, the steeper the line must be.A position-time graph makes it simple to determine the average velocity of a moving item. The change in location (represented by Δd) divided by the corresponding change in time (represented by Δt) is the average velocity:Velocity=Δd/Δt
A position-time graph, which depicts time on the x-axis and location with relation to the beginning point on the y-axis, can be used to visualise motion.A position-time graph's slope is a measure of velocity. The rate of change of motion increases with slope steepness.A position-time graph can be used to determine average velocity, which is equal to the change in position divided by the corresponding change in time.To know more about Position -Time Graph,Refer to:
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5. If 20kg body falls down ward freely from 40m building, find the kinetic energy of this body when at a height of 30m above the ground.
The kinetic energy of the body at 30m above the ground will be 1960 joules.
First, We have to calculate the final velocity when the object is 30m above the ground. We know that :
[tex]v^{2} + u^{2}[/tex]= 2as , where v is the final velocity, u is the initial velocity, s is the displacement and a is the acceleration . Since the body is dropped , the initial velocity will be 0 and a = 9.8m/s (acceleration by gravity), and since the body is 30m above the ground the displacement achieved by it will be 40-30 = 10m
∴ [tex]v ^{2} =[/tex] 2as
⇒[tex]v^{2}[/tex] = 2 x 9.8 x 10
⇒[tex]v^{2}[/tex] = 196
We can directly use this value to find the kinetic energy of the system. We know that kinetic energy is [tex]\frac{1}{2} m v^{2}[/tex].
⇒ 1/2 x 20kg x 196
⇒1960
∴ Kinetic system of the body from 30m above the ground will be 1960 joules
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At takeoff a commercial jet has a 65.0 m/s speed. Its tires have a diameter of 0.550 m.
(a) At how many rpm are the tires rotating?
X rpm
(b) What is the centripetal acceleration at the edge of the tire?
x m/s²
(c) with what force must a determined 10-15 kg bacterium cling to the rim?
N
(d) Take the ratio of this force to the bacterium's weight.
X (force from part (c)/bacterium's weight)
(a) Angular speed = 1344.8 revs per minute
(b) Centripetal acceleration is equal to 8473.4 m/s2.
Force = 8.4734 10-12N in (c).
(d) The force-to-weight ratio for bacteria is 864.6.
How to find the Calculation?The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case.
(A) Angle speed (w) = volume/radian
d=0.850m, r=0.850m/2, and v=60m/s=0.425m
w = 60/0.425 = 141.2rad/s, which is equal to 141.29.524 rev/min, or 1344.8 rev/min.
(b) Centripetal acceleration is calculated as follows: w2r = 141.2 0.425 = 8473.4 m/s2.
The rate of change in velocity is known as acceleration. Acceleration typically signals a change in speed, though this is not always the case.
(c) Force Equals mass centripetal acceleration, which is 1/1015 8/773.41 = 8.4734/10-12N.
(d) The weight of a bacterium is calculated as follows: mass acceleration due to gravity = 1 10-15 9.8 = 9.8 10-15N
Force to bacteria weight ratio is 8.473410-12N/9.810-15N, or 864.6.
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At which of the following locations in the nuclear power plant would an accident most likely result in the release of fission products? The reactor vessel holds the uranium fuel that is undergoing fission reactions that result in heat production.
A nuclear accident would most likely result in the release of fission products from the containment building, which is designed to contain radiation from a nuclear accident.
What is radiation?Radiation is the emission or transmission of energy in the form of electromagnetic waves (such as gamma rays and X-rays), particles (such as alpha particles and beta particles), or acoustic waves (such as ultrasound). Radiation is a form of energy that is all around us, in the air we breathe, the food and water we consume, and even in our own bodies. Different types of radiation have different properties and effects on living organisms. Types of radiation include ionizing radiation, which can cause cell damage and can be hazardous to living organisms, and non-ionizing radiation, which is generally considered harmless.
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Gansbsvskssvs oh alas no velwsjshe St h oh dog oh set of
The inverse of the mass is referred to as acceleration. The acceleration will be slower the more mass there is.
How does acceleration work?Acceleration is the rate of change in an object's velocity over time in mechanics. One of the vector quantities is speed. The direction of the net force exerted on an object is what determines its acceleration. The change in velocity rate is referred to as acceleration. Usually, but not always, acceleration implies a change in velocity.
A circular object moving at a constant velocity is still accelerating because its velocity is changing in the opposite direction. In physics, acceleration is the rate of change in an object's velocity over time. According to Newton's second law, the sum of all forces acting on an object determines its acceleration. Meters per second (ms²) is the SI unit for acceleration.
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Which of the following statements are true of the horizontal motion of a projectile? Select all that apply.-the horizontal velocity is a constant value.
-the horizontal acceleration is o m/s^2.
-there are no horizontal forces acting upon the object.
The horizontal velocity of a projectile with a horizontal component of motion will never change. At the top of its trajectory, a projectile's horizontal velocity is zero meters per second.
What does motion imply? Simply put?
Motion is the slow, long-term shift in an object's location. Motion is defined in terms of displacement, distance, momentum, acceleration, time, and speed. Motion can be experienced while walking, cycling, leaping, bathing, eating, drinking, playing, typing, watching moving cars, and tossing a ball.
Why is movement important to your well-being?
Motionless is death. As much as it needs food, water, or air, your body needs movement. It provides the brain with the essential nutrients it needs to be stimulated (known as proprioception).
The vertical and horizontal velocities of a projectile are independent of one another; the horizontal velocity is unaffected by the vertical velocity.
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A student investigated heat transfer using a bottle of water. The student placed the bottle in a room at 20.5DC. The student measured the temperature of the water in the bottle at 7 a.m. and again at 3 p.m. The data from the investigation are shown in the table below.Compare the average kinetic energy of the water molecules in the bottle at 7 a.m. to the average kinetic energy of the water molecules in the bottle at 3 p.m.
The molecule were increased in kinetic energy but in a random structure. Thus, option 2 is correct.
Which of the seven types of energy can be seen in practice?Energy can take many different forms. Some examples of these are: nuclear and atomic energy, thermal energy, energy of motion, gravitational energy, electrical energy, elastic energy, fuel cells, and so on.
What kinds of real-world uses are there for thermal energy?Things are heated, water is boiled, eggs are fried, and metal is melted for automobile construction. Heat is converted into electricity at a thermal power plant, which powers our daily activities. The term "temperature" refers to the degree to which something is hot or cold. The temperature is measured in degrees Celsius.
Given:
At 3 p.m., the water temperature is raised.
The average kinetic energy of an object is proportional to its temperature. As a result, as temperature rises, so does average kinetic energy. Kinetic energy is caused by the random movement of molecules.
Correct answer: The kinetic energy of the molecule was increased, but in a random structure.
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Complete question:
The sales S (in thousands of units) of a new product after it has been on the market for t years is given by S = Cek/t . (a) Find S as a function of t when 5000 units have been sold after 1 year and the saturation point for the market is 30,000 units (that is, tlim[infinity] S = 30). (b) How many units will have been sold after 5 years?
(a) [tex]\mathbf{S = 30,000e^{(-k/t)}}[/tex] & (b) [tex]\mathbf{S = 30,000e^{(-k/5)}}[/tex] are the number of units that will have been sοld after 5 years is [tex]\mathbf{30,000e^{(-k/5)}}[/tex], as per the sales S (in thousands of units) of a new product after it has been οn the market for t years is given by S = Cek/t .
What is cumulative sales?
Cumulative sales is the total amοunt of sales earned in a given period of time. It is the sum of all sales made during a specific periοd, including all sales before and during the current period. Cumulative sales is a measure of οverall performance and progress. It allοws businesses to identify trends in their sales and perfοrmance οver time.
Given that 5000 units have been sοld after 1 year and the saturation pοint for the market is 30,000 units, we can write the equatiοn S = Cek/t as follοws:
[tex]\mathrm{30,000 = 5000e^{(k/1)}}[/tex]
Rearranging this equatiοn, we get:
[tex]\mathrm{e^{(k/1)}=6}[/tex]
Therefore, k = ln(6)
Substituting this value of k intο the equation S = Cek/t, we get:
[tex]\mathrm{S = 30,000e^{(-ln(6)/t)}}[/tex]
Simplifying this equatiοn, we get:
[tex]\mathrm{S = 30,000e^{(-1/t)}}[/tex]
Therefore, [tex]\mathrm{S = 30,000e^{(-1/t)}}[/tex] is the equation for the sales S (in thousands of units) of a new product after it has been οn the market for t years when 5000 units have been sοld after 1 year and the saturation point for the market is 30,000 units.
To find the number of units that will have been sοld after 5 years, we can substitute t = 5 into the equatiοn [tex]\mathrm{S = 30,000e^{(-1/t)}}[/tex]. This gives us:
[tex]\mathrm{S = 30,000e^{(-1/5)}}[/tex]
Therefore, the number of units that will have been sοld after 5 years is [tex]\mathbf{30,000e^{(-k/5)}}[/tex]
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a driver in a car traveling at a speed of 34.7 mi/h sees a deer 114.5 m away on the road. assuming the deer does not move, what is the minimum constant acceleration necessary for the car to stop without hitting the deer? note that 1 mi
The minimum constant acceleration necessary for the car to stop without hitting the deer is -8420.21 mi/h^2. The negative sign means that the car is deaccelerating.
Is it feasible to accelerate continuously?Consider a particle traveling uniformly in a circle; it experiences acceleration since the motion's direction is changing, but it maintains a constant speed along the tangential axis throughout the motion. Yes, it is feasible to have to change speed and constant acceleration.
What is speed and what is its unit?The pace at which a distance changes over time is referred to as speed. It has a dimension of time distance. As a result, the fundamental unit of time and the basic unit of distance are combined to form the SI unit of speed. As a result, meters per second is the SI unit of speed.
Given:
Speed = 34.7 mi/h
Distance = 114.5 m = 114.5 m×0.000621371 = 0.0715 mi
[tex]V_f=V_i+2ad[/tex]
[tex]0=34.7^2+2a*0.0715[/tex]
[tex]0.143a=-1204.09[/tex]
[tex]a=\frac{-1204.09}{0.143}[/tex]
[tex]a=-8420.21mi/h^2[/tex]
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For the following exercises, find the measure of the angle between the three-dimensional vectors a and b. Express the answer in radians rounded to two decimal places, if it is not possible to express it exactly.a = 3i - j - 2k, b = v + wwherev = -2i - 3j + 2k and w = i +2k
The measure of the angle between three-dimensional vectors a and b; θ = acos(-0.5235) = 2.0463 radians, rounded to two decimal places.
What is meant by vectors?In physics, vector is that quantity that has both direction and magnitude.
As, cos(θ) = (a · b) / (||a|| * ||b||)
Given, a = 3i - j - 2k, b = v + w where v = -2i - 3j + 2k and w = i +2k
So, a · b = (3i - j - 2k) · (v + w) = (3i - j - 2k) · (-2i - 3j + 2k + i + 2k)
a · b = (3i - j - 2k) · (-2i - 3j + 2k + i + 2k) = (-6i^2 + ji - 4ik) + (-3j - 2k + i + 2k) = -6 + 1 - 4 + (-3 - 2 + 1 + 2) = -4
||a|| = sqrt((3i - j - 2k) · (3i - j - 2k)) = sqrt(9 + 1 + 4) = sqrt(14) = 3.74166
||b|| = sqrt((v + w) · (v + w)) = sqrt((-2i - 3j + 2k + i + 2k) · (-2i - 3j + 2k + i + 2k)) = sqrt((-2i - 3j + 2k + i + 2k) · (-2i - 3j + 2k + i + 2k)) = sqrt((-4 - 6 + 4 + 1 + 4)) = sqrt(9) = 3
cos(θ) = (a · b) / (||a|| * ||b||) = -4 / (3.74166 * 3) = -0.5235
Hence, θ = acos(-0.5235) = 2.0463 radians, rounded to two decimal places.
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____is a measure of the random motion of particles. ____is the transfer of energy between two objects due to temperature difference.
Temperature is a measure of the random motion of particles and heat is the transfer of energy between two objects due to temperature difference.
What do you call a measure of particle movement?
Temperature can be used to calculate the kinetic energy of particles moving within a substance, or, to put it another way, a substance's temperature affects the kinetic energy of its particles.Because molecules in a system move randomly, thermal energy also known as random or internal kinetic energy is produced.In joules, heat is measured (J). Heat is a form of energy transfer, which explains this. In degrees Celsius (°C), temperature is a unit of measurement for how hot or cold a substance feels. Temperature is a gauge for an object's average particle kinetic energy.To know more about temperature visit:
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The velocity (in meters/sec) of a particle moving along a straight line is given by v(t)=2t^2 + 3t - 1 where t is measured in seconds.
Answer the following questions given that the initial position s (0) =
Despite the fact that it was screwed up in, the displacement will be S of seven minus.
What is the initial position s (0) ?The goal is to make the position at Times Two equal to 4. This just serves to plug in four for tea. We're going to assess this and see if we can repeat the amount after we just typed in for everywhere for T. That is the current situation. T is equal to 4, therefore that's what it is. The location would be helpful to us. The concept is the same. It is seven times a third. Seven squared plus seven plus six equals that. You may calculate this to obtain 25 0.3 repeating. We want to determine a particle's displacement. It appears to have taken place between the hours of 4 and 7. Despite the fact that it was screwed up in, the initial position will be S of seven minus.To learn more about initial position refer to:
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A 22.5 kg person climbs up a uniform ladder with negligible mass. The upper end of the ladder rests on a frictionless wall. The bottom of the ladder rests on a floor with a rough surface where the coefficient of static friction is 0.11. The angle between the horizontal and the ladder is θ . The person wants to climb up the ladder a distance of 0.65 m along the ladder from the ladder’s foot.
What is the minimum angle θmin (between the horizontal and the ladder) so that the person can reach a distance of 0.65 m without having the ladder slip?
The acceleration of gravity is 9.8 m/s².
Answer in units of °.
Answer:
62°
Explanation:
Variables:
x=0.65m (distance up ladder)
L=2.5m (ladder length)
m = 22.5kg (mass)
g = 9.8 (gravity)
μ = 0.11 (static friction)
N = Normal Force (Weight in this context)
Formulas:
Weight(W)=mg
Friction Force(F)=μN
Torque(T)= [tex]Frsin[/tex]θ
Substitute Force and length in each torque we're calculating
[tex]T_{counterclockwise} =[/tex] (μN)*L*sinθ
[tex]T_{clockwise} =[/tex] mg*x*cosθ
They need to be equal:
[tex]T_{counterclockwise} = T_{clockwise}[/tex]
(μN)*L*sinθ = mg*x*cosθ
[tex]\frac{sin}{cos}=tan[/tex]
tanθ= (mg*x) / (μ*N*L)
Since W=mg=N, they cancel out.
tanθ= (x) / (μ*L)
Inverse tangent
θ= [tex]tan^{-1}[/tex](x / (μ*L))
Plug in variable:
θ= [tex]tan^{-1}[/tex](0.65 / (0.11*2.5))
θ= [tex]tan^{-1}[/tex](2.3636)
θ= 62.0676° ≈ 62°
Hope this helps ;)
geologymagnetic reversals of the earth's magnetic field are when the earth's magnetic poles change direction
Geologymagnetic reversals of the earth's magnetic field are when the earth's magnetic poles change direction: False.
What is geomagnetic reversal?Change in a planet's magnetic field such that the positions of magnetic north and magnetic south are interchanged is called a geomagnetic reversal.
During an excursion or a reversal, magnetic field is considerably weakened and allows many cosmic rays to reach the surface of the planet. These energetic particles from space can be damaging to life on Earth if too many of them reach the surface.
Without magnetic field around the Earth, life could not exist on the planet. Solar radiation would strip away the atmosphere.
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Two candles of the same length are made of different materials so that one burns out completely at a uniform rate in 3 hours and the other in 4 hours. At what time should the candles be lit so that at 4 PM, one stub is twice the length of the other?
The candles should be lit at 12 PM (noon) for the stub of the first candle to be twice the length of the second candle at 4 PM.
How can we conclude so.To determine the time at which the candles should be lit so that at 4 PM one stub is twice the length of the other, we need to use the concept of similar triangles.
Let's call the length of the first candle (the one that burns out in 3 hours) as x. The length of the second candle (the one that burns out in 4 hours) as y.
At 4 PM, the first candle will have burnt out completely, while the second candle will have only burnt out (4/3) of its length.
So, the length of the stub of the second candle is y(4/3). Now we know that x = 2(y(4/3))
We can solve for x and y by using the proportion (x/3 = y/4).
Comparing both equations we can conclude that the first candle should be lit at 12:00 PM in order to fulfill the condition.
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carbon dioxide could also be your answer if you dont have water
Answer: The human breathing mechanism actual revolves around CO2, not oxygen. Without carbon dioxide, humans wouldn't be able to breathe.
Explanation:
vague question - i tried to answer as best as i could
basic conceptual ideas and basic algebraic calculations of sound wave theory (e.g., superposition, constructive and destructive interference, beats, doppler effect, wave velocity equation, speed of sound in various media, standing waves, reflection, refraction, diffraction, propagation).
Sound wave theory encompasses several basic conceptual ideas and algebraic calculations, including Superposition The principle that when two or more waves overlap, the resulting amplitude at a specific point is the sum of the amplitudes of the individual waves.
What are the basic conceptual ideas and basic algebraic calculations of sound wave theory?Constructive and destructive interference: When two waves are in phase, they reinforce each other (constructive interference) resulting in a larger amplitude. When two waves are out of phase, they cancel each other (destructive interference) resulting in a smaller amplitude or no amplitude.Beats: The fluctuation in sound intensity that occurs when two waves of slightly different frequencies are superimposed.Doppler Effect: The change in frequency of a wave due to the relative motion of the source and observer.Wave velocity equation: The equation that relates the wavelength, frequency, and velocity of a wave. It is v=λf, where v is the velocity, λ is the wavelength, and f is the frequencySpeed of sound in various media: Sound travels at different speeds in different materials, such as air, water, and solids.Standing Waves: A wave that oscillates in a fixed position, often observed in closed systems like strings or air columns.Reflection: The bouncing back of sound waves when they hit a surface.Refraction: The bending of sound waves as they pass through a medium with different densities.Diffraction: The bending of sound waves as they pass around an obstacle or through an opening.Propagation: The movement of sound waves through a medium.In summary, Sound wave theory encompasses several basic conceptual ideas and algebraic calculations, including superposition, constructive and destructive interference, beats, Doppler effect, wave velocity equation, speed of sound in various media, standing waves, reflection, refraction, diffraction, and propagationTo learn more about sound wave refer:
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C. propan-1-one D. pentan-1-ol Question 2 ceiling -↑ 1,8 m 3,5 m mais (2) [12] A girl stands on a table in a classroom. She throws a ball of 0.2 kg vertically downwards to the floor hoping that the ball, after it bounced on the floor, will hit the the classroom. of She throws the ball with a velocity of 8 m.s-1 from a height of 1,8 m above the floor. Ignore the effects of friction. Write down the magnitude and direction of the acceleration of the ball immediately after ball left her hand. ( Is the ball in free fall while it moves downwards? Answer YES or NO and give an explana for the answer. Calculate the magnitude of the velocity with which the ball hits the floor.
2.1. The acceleration of the ball immediately after it leaves the girl's hand is -9.8 m/s², directed downwards.
2.2. Yes, the ball is in free fall while it moves downwards. This is because the only force acting on the ball is gravity, which is a constant downward force.
How to calculate the magnitude of velocity?The magnitude of the velocity with which the ball hits the floor can be calculated using the equation v² = u² + 2as, where u is the initial velocity, a is the acceleration, v is the final velocity, and so is the distance traveled. In this case, u = 8 m/s, a = -9.8 m/s², and s = 1.8 m. Plugging these values into the equation, we get v = √ (8² - 2 × (-9.8) × 1.8) = √ (64 + 35.28) = √ (99.28) = 9.96 m/s.The time it takes for the ball to hit the floor can be calculated using the equation t = (v-u)/a, where t is the time, v is the final velocity, a is the acceleration and u is the initial velocity. In this case, v = 9.96 m/s, u = 8 m/s, and a = -9.8 m/s². Plugging these values into the equation, we get t = (9.96 - 8)/-9.8 = 1.97 s.
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