When two objects of different masses are subjected to a force of the same strength, the one with less mass will experience a higher change in velocity.
What occurs when two items hit each other?Each object pulls the other when two objects come into contact. Imagine using a bat to strike a softball. The ball is pushed away by the bat when it collides with it. The bat experiences force from the ball as well.
What happens when two moving objects slam into each other?Even if two colliding objects have masses that are very different from one another, they will nevertheless exert equal forces on one another. An object always experiences an impetus and a shift in momentum during a collision. The impulse that an object encounters during a collision is equal to its variation in speed.
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"the horizontal surface on which the block slides is frictionless. the speed of the block before it touches the spring is 6.0 m/s. how fast is the block moving at the instant the spring has been compressed 15 cm? (assume k = 2.0 kn/m.)"
The block is moving at the speed of 5.61 m/sec at the instant the spring has been compressed 15 cm. If the mass possessed by the block is 10 kg.
Let the mass of the block, m = 10 kg
Speed of the block before touching the spring, v = 6.0 m/s
Let the speed of the block after compressing the spring = V
k = 2.0 KN/m
By the law of conservation of energy,
0.5mv² = 0.5kx² + 0.5mV²
10 × 6² = 2000 × 0.15² + 10 × V²
V² = (10 × 6² - 2000 × 0.15²)/10
V² = 31.5
V = 5.61 m/s
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Identify the heat transfer method involved when wind is blowing heat from the fire towards a stand of thick brush.
The heat transfer method involved when the wind is blowing the heat from the fire towards the stand of the thick brush is called convection.
Convection transfers heat by moving liquids or gases. Wildfires typically produce rising columns of gas accompanied by sparks, embers, and burning twigs. These convection columns move downwind of the firefront and carry the embers that serve as the starting point for the fire. This movement of heat energy away from the ground by vertical air movement is called "free convection" or "natural convection." Hot air balloons rise because warm air/wind is less dense than cold air.
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a student measures the volume of a liquid using a measuring cylinder. what else needs to be measured by the student in order to determine the density of the liquid
A. depth of the liquid in the cylinder
B. mass of the cylinder
C. mass of the liquid
D. temprature of the liquid
pls it's urgent Tuesday's the deadline
Answer:
Mass of the liquid (C)
Density is the ratio of mass to volume
ound travels at 343m/s in the air. what distance from the student, in meters, is the lightning strike?
If it took 5.5 seconds for the sound of the lightning strike to reach the student, then the distance of the lightning strike from the student is 1886.5 meters.
To determine the distance from the student to the lightning strike, you would need to know the time it took for the sound of the strike to reach the student. The speed of sound in air is approximately 343 meters per second (m/s). By using the formula:
distance = speed x time
If it takes 5.5 seconds for the sound of the lightning strike to reach the student, then the distance of the lightning strike from the student is:
distance = 343 meters/second × 5.5 second
distance = 1886.5 meters
Therefore the distance is 1886.5 meters.
Also, keep in mind that the speed of sound varies with temperature, humidity, and pressure. So, if you want to get an accurate result, you'll need to take these factors into account as well. Furthermore, it's important to remember that sound travels in a straight line, so it's not always the same distance as the visual distance of the lightning strike.
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Your question seems incomplete, but i assume the complete question was:
"Sound travels at 343m/s in the air. What distance from the student, in meters, is the lightning strike if it took 5.5 seconds for the sound of the lightning strike to reach the student?"
Two 1.70 kg balls are attached to the ends of a thin rod of length 70.0 cm and negligible mass. The rod is free to rotate in a vertical plane without friction about a horizontal axis through its center. With the rod initially horizontal (the figure), a 32.0 g wad of wet putty drops onto one of the balls, hitting it with a speed of 1.56 m/s and then sticking to it. (a) What is the angular speed of the system just after the putty wad hits
The end of the a thin rod with a length of 0.452 m and very little mass is moving up the plane at an acceleration of 0.80 m/s2 whereas the rod is horizontal.
Two distinct formulas are used to determine the angular speed,The speed of an object in rotation is known as its angular speed. In radians, the distance traveled is denoted by the symbol. The amount of time is expressed in seconds. As a result, the angular speed is expressed in radians per second, or rad/s.
Is angular speed and angular velocity equivalent?A scalar measurement of the rotating item is its angular speed. A vector representation of the rotational motion is the angular velocity. Only the magnitude of an angle's speed is specified. The magnitude and direction are both specified by angular velocity.
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after the collision, the stick and puck will rotate about their combined center of mass. how far is this center of mass from the point at which the puck struck?
The distance from the point of collision to the center of mass of the stick and puck will depend on the mass of the stick and puck, and their relative positions at the time of collision.
The center of mass (COM) of an object is the point at which all of its mass is concentrated, and around which it rotates. The COM of two or more objects is the point at which the masses of the objects balance each other.
In the case of a collision between a stick and a puck, the COM of the two objects will be located at a point where the distance from the COM to the point of collision is proportional to the mass of the object. This means that if the stick and puck have different masses, the COM will be closer to the more massive object.
To know the exact distance of the center of mass from the point of collision, more information is needed like mass and the relative positions of both objects before the collision.
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sirius is a blue-white star with a surface temperature of about 9800 k. what is most likely the mass of sirius?
sirius is a blue-white star with a surface temperature of about 9800 k. 2.0 solar mass is most likely the mass of sirius.
What do mass and an example mean?The amount if matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. Examples of objects with mass include a table, a desk, your bedroom, a football, weight glass, and even air.
How is mass determined?Scientists frequently use balances to quantify mass. Using an electronic balance or a beam balance, one may directly determine the mass of solids. A liquid's mass can be calculated by measuring its volume and using the density table to determine the liquid's density. The kilogram is the SI measure of weight (Kg).
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assume the motions and currents mentioned are along the x axis and fields are in the y direction.
(a) Does an electric field exert a force on a stationary charged object?
Yes/No
(b) Does a magnetic field do so?
Yes/No
(c) Does an electric field exert a force on a moving charged object?
Yes/No
(d) Does a magnetic field do so?
Yes/No
(e) Does an electric field exert a force on a straight current-carrying wire?
Yes/No
(f) Does a magnetic field do so?
Yes/No
(g) Does an electric field exert a force on a beam of moving electrons?
Yes/No
(h) Does a magnetic field do so?
Yes/No
Electric field is a physical field occupied by a charged particle on another particle in its surrounding. It is denoted by E. It is an invisible field.
a) Yes, an object with charge q experiences force from an electric field of intensity E. This force still acts even when the item is stationary because, as we can see, it is independent of the speed of the object.
b) No, the magnetic force produced by an object with charge q and speed v is equal to the magnetic force produced by an object with charge q and speed v in a magnetic field of intensity of B.
c) The electric force is still very strong. Point (a) shows that the electric force is still present and unaffected by the charge's speed.
d) The magnetic force F is no longer zero because the object is now moving at a specific speed v.
e) The answer is that the electric field does exert a force on the charges moving along the wire because it does so constantly to a charge.
f) Because a magnetic field always exerts a force on a moving charge, the charges flowing through the wire are being affected by the magnetic field. This is because the current in the wire is made up of charges travelling at a constant v.
g) Since an electric field exerts force and electrons have an electric charge, this argument makes sense. As a result, an electric charge and, by extension, an electron beam are always under the influence of an electric field.
h) The magnetic force is constant since the speed of the electrons in the beam is constant (v). V is not equal to zero, hence the magnetic field is not zero either.
As a result, an object with charge q experiences a force from an electric field of intensity E. This force still acts even when the item is stationary because, as we can see, it is independent of the speed of the object.
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A clear, colorless, crystalline solid is heated. A pale yellow-green gas is given off and a shiny, malleable metal was left behind.
When a crystalline solid that is transparent, colorless, and heated. A chemical shift is seen when a light yellow-green gas is released and a glossy, malleable metal is left behind.
Chemical synthesis, or, alternatively, chemical breakdown into two or more separate molecules, occurs when one material reacts with another to create a new substance. These processes are referred to as chemical reactions, and they are often irreversible barring additional chemical reactions. Exothermic processes are those that generate heat; endothermic reactions, on the other hand, are those that may need heat in order to proceed. The science of chemistry places a lot of emphasis on comprehending chemical changes.
A clear, colorless, crystalline solid is heated. A pale yellow-green gas is given off and a shiny, malleable metal was left behind is an example of chemical change.
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during spring semester at mit, residents of the parallel buildings of the east campus dorms battle one another with large catapults that are made with surgical hose mounted on a window frame. a balloon filled with dyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room. assume that the stretching of the hose obeys hooke's law with a spring constant of 100 n/m. if the hose is stretched by 5.00 m and then released, how much work does the force from the hose do on the balloon in the pouch by the time the hose reaches its relaxed length?
The work is found to be =1.25×10 3 J. if a spring constant of 100 n/m. if the hose is stretched by 5.00 m and then released .
How do u define work?Work is force applied over distance. Examples of work include lifting an object against the Earth's gravitation, driving a car up a hill, and pulling down a captive helium balloon. Work is mechanical manifestation of energy. The standard unit of work is the joule ,equivalent to a newton.
Why do we define work?The definition of work in physics reveals its relationship to energy whenever work is done, energy is transferred. Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
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a sample of blood is placed in a centrifuge of radius .15 m. the mass of a red corpuscle is 3.0 x 10-16 kg, and the magnitude of the force required to make it settle out of the plasma is 4.0 x 10-11 n. what does the angular speed need to be?
A red corpuscle mass 3.0 10-16 kg, and 4.0 10-11 N of force is necessary for it to pull away from the plasma. Angle of rotation = = /t.
What does it mean in mass?In physics, mass is a statistical expression of inertia, a basic characteristic of all matter. It essentially refers to a body of matter's resistance to changing its speed or location in response to the administration of a force.
What do mass and an example mean?The sum of matter that makes up every object or body is the greatest way to understand mass. Everything that we can see has mass. For instance, even air has mass, as does a table, a desk, your sofa, a game, a glass, etc.
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An electron is projected with an initial speed into the uniform field between two parallel plates (Fig. E21.27). Assume that the field between the plates is uniform and directed vertically downward and that the field outside the plates is zero. The electron enters the field at a point midway between the plates. (a) If the electron just misses the upper plate as it emerges from the field, find the magnitude of the electric field. (b) Suppose that the electron in Fig. E21.27 is replaced by a proton with the same initial speed Would the proton hit one of the plates
The magnitude of the electric field is found to be 364N/c.
What does a consistent electric field look like between two parallel plates?That's because the distance between the plates is assumed to be very small in comparison to their combined area, the electric field between parallel plates is uniform and nearly constant. Due to the interplay of the two plates' fields, the field is roughly zero outside of the plates. Equation E = V/d can be used to determine the magnitude of this type of homogeneous electric field because the field lines are parallel to one another.
y- direction = 0.005m
x direction t 2m distance => vo = 1.6 x 10^6m/s
Time of flight => t = 2m/1.6 x 10^6m/s
=> 1.25 x 10^-8 s
y=voy t + 1/2 a t^2
0.005 = 1/2 a (1.25 x 10^-8 )^2
a=> 6.4 x 10^13m/s2
a = F/m = eE/mof electron
=> 9.1 x 10^-32 x 6.4 x 10^13 m/s2/ 1.6 x 10^-19C
=> 364N/c
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a body of mass m is thrown at an angle theta with the horizontal with an initial velocity v0. find the mean power developed by gravity over the whole time of motion of the body
A body of mass m has been thrown with an initial position of v0 at an angle θ with the horizontal. determine the average force that gravity develops over
Describe a motion response?The steady shift in an object's location over time is known as motion. Movement, distance, velocity, acceleration, time, and speed are used to define motion.
Which of the two motions are they?Motion can be classified as translational, rotational, periodic, or non-periodic. Translational motion is a type of motion where all components of an item by the same amount in the same amount of time.
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Determine the terminal voltage of each battery in the figure. Part A Determine the terminal voltage of top battery. Express your answer to two significant figures and include the appropriate units. 1 of 1 Figure r = 2.0 22 M4 8 = 18 V Vierminal < R= 6.622 P = 1.092 Submit Recuest Answer &= 12v Part B Determine the terminal voltage of bottom battery Express your answer to two significant figures and include the appropriate units.
Terminal voltage of top battery and bottom battery are found to be 13.82V and 10.43V.
What are internal resistance and terminal voltage?The terminal voltage of a cell is the potential difference between its electrodes when current is extracted from it. The internal resistance of the cell is the resistance provided to the flow of electric current through it by the electrolyte inside.
Terminal voltage of top battery:
current I = 18/(2+6.6)
=> 2.09A
Terminal voltage = E - Ir
=> 18 - (2.09 x 2)
= 13.82V
Terminal voltage of bottom battery:
current I = 12-(1+6.6) = 1.57A
Terminal voltage = 12 - (1.57 x 1)
=> 10.43V
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The truncated right circular cone below has a large base radius 8 cm and a small base radius of 4 cm. The height of the truncated cone is 6 cm. The volume of this solid is $n \pi$ cubic cm, where $n$ is an integer. What is $n$
According to the information, we can infer that the volume of this solid is 703.7 cm³.
How to calculate the volume of this solid?To calculate the volume of this solid we have to use the following formula and know this data (both base radius and height). So, if we read the statement, we can find all the neccesary information to complete this task.
Information:
Large base radius: 8cmSmall base radius: 4cmHeight: 6 cmTo use the formula, we have to replace values of R and r (R represents large base radius and r represents small base radius).
Formula:
V = pi * ( height / 3 ) ( R² + Rr + r²) V = 3.1416 * (6/3) (8² + 8*4 + 4²)V = Pi * (2) (64 + 32 + 16)V = 2Pi * 112V = 224 * Pi cm³V = 703.7 cm³According to the above, the volume of this solid is 703.3 cm³.
Note: This question is incomplete because there is some information missing. Here is the complete information:
Attached image
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1. the filament of a standard 100-w light bulb has a resistance of about 100 ohms. for this laboratory the glass of the light bulb is unfrosted, so that the filament can be viewed directly. the light bulb is connected to a variable ac voltage source (a variac), which can deliver up to 140 volts ac. when the voltage is low, about 20 volts, the filament is a dull, red color. when the voltage is high, 100 v, how does the filament appear? explain why. hint: at a higher filament temperature, photons with higher energies can be emitted in addition to low energy photons.
With a little additional arithmetic, we can determine that resistance of the filament at 100 watts is roughly 145 ohms using the formula R(Resistance)=E(Voltage)/I(Amps).
How is resistance calculated for a 100 watt bulb?The bulb's power rating is 100 watt, and the rms voltage from across bulb is 220 volts, according to the query. So, to find the resistivity of the bulb, change P=100 watts with Vrms=220 watts in the formula P=V2rmsR. As a result, the bulb has a 484 ohm resistance.
What is the formula for resistance?The ratio of the electric current flowing through it to the voltage applied is the definition of electrical resistance for a component in the circuit or device: if there is consistent resistance over a broad range
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A light bulb is 60cm from a concave mirror with a focal length of 20cm. Use ray tracing to determine the location of its image. Is the image upright or inverted? Is it real or virtual. Verify your results by doing the calculations.
Ray tracing is a method used to determine the location and characteristics of the image created by a mirror.
To solve this problem, first draw a ray diagram to help visualize the situation. In this diagram, draw a line from the light bulb to the center of the mirror, which is the focal point. Then draw a ray that reflects off the mirror and back towards the focal point. This ray is called the principal ray.
Using the principal ray, you can draw a line that is parallel to the principal ray and intersects the focal point. This line will intersect the mirror at a point that is the same distance from the mirror as the light bulb is from the focal point. This is the location of the image.
To determine whether the image is upright or inverted, draw another ray from the light bulb, parallel to the principal ray. If this ray reflects off the mirror and intersects the focal point, then the image is upright, and if it reflects off the mirror and does not intersect the focal point, then the image is inverted. In this case, the image is inverted.
To determine if the image is real or virtual, draw a line from the image to the center of the mirror. If this line intersects the mirror, then the image is real, and if it does not intersect the mirror, then the image is virtual. In this case, the image is virtual.
To verify these results, you can calculate the location of the image using the mirror equation: 1/f = 1/d1 + 1/d2, where f is the focal length, d1 is the distance from the light bulb to the mirror, and d2 is the distance from the image to the mirror. Plugging in the values from this problem, we get 1/20 = 1/60 + 1/d2, which simplifies to d2 = 120 cm. This confirms that the image is 120 cm from the mirror, which is the same location as determined by ray tracing.
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what mass flow (in kg/d) of ammonium-n passes by any point in the lake after these two sources have become mixed?
The mass flow of ammonium-n passed by any point in the lake after the two sources have become mixed depends on the combined rate of release from the sources.
What is the mass ?
The amount of matter that makes up a thing is measured by its mass.. It is typically measured in kilograms or grams and is an important quantity in physics and chemistry. Mass is different from weight, which is a measure of the force of gravity on an object. Mass is an intrinsic property of an object, meaning it is independent of the object's environment. Mass is conserved, meaning it cannot be created or destroyed, only changed through physical or chemical reactions.
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net work w would accelerate an object of mass m to velocity v. what net work is needed to accelerate an object of mass 2m from rest to velocity v?
Net work done 2w is needed to accelerate an object of mass 2m from rest to velocity v.
What is work done?The force that is required to move a thing a specific distance is referred to as the work done. Essentially, it is a measurement of the amount of energy that is transmitted to or from an item so that it can be moved. The result of the displace and or the component of such force applied of the particle in the displacement direction is the definition of the work performed by a force. Work is accomplished when we remove a block with a few force; the body moves more quickly. Work completed is noted as.
as we know that work done = 1/2 mv^2
as we double the m then work done will aslo become double because work done is directly proportional to the mass .
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give answer in points
What is the difference between potential difference and electromotive force (e.m.f)?
Answer:
The electromotive force is the amount of energy given to each coulomb of charge. The potential difference is the amount of energy utilized by one coulomb of charge. The electromotive force is independent of the circuit's internal resistance. The potential difference is proportional to the circuit's resistance.
g objects and possessions can become viewed as part of the self when individuals are able to exercise power and control over them in much the same way as they control the actions of an arm or a leg describes what?
This describes the concept of self-extension. When individuals are able to exercise power and control over objects and possessions, they may begin to view these things as extensions of themselves.
What impact do possessions have on a person's sense of self?We may understand and express our self-identity through our possessions. When opportunities for receiving external validation of self are scarce, as can be the case as a result of institutionalization, for the elderly, things serve as crucial archives of memories of one's self-identity in the past.
What type of self-concept considers possessions to be the natural extensions of the self?William James claimed that the things, places, or even persons that carry the label "my" are what make up the material self. These things are seen as extensions of people's identities. For instance, your clothing, which you refer to as "my wardrobe," expresses certain facets of your personality.
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how does pressure at the bottom of a body of water relate to the weight of water above each square meter
The pressure at the bottom of a body of water is the weight of water per one-meter square area.
The force applied perpendicularly to an object's surface per unit area across which that force is dispersed is known as the pressure. The definition of it is force per unit area. It is usually more convenient to use pressure rather than force to describe the influences upon the behaviour of fluid. various units are used to express pressure.
In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. As a result, the bottom of a fluid column suffers more pressure than the top, as does an object submerged in the column.
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10) The period of a pendulum is the time it takes to complete a full swing. For this picture, it would be the time taken to swing from point A to point C, and then back to point A. Above you can see the equation for describing this time period. It is counterintuitive, but, based on this, you can see that changing the mass of the bob would
Have no affect on the period of the pendulum. This is because the equation does not include the mass, which means that the period of the pendulum is independent of the mass of the bob.
What is the pendulum ?
A pendulum is a weight suspended from a pivot so that it can swing freely. It is a device used to measure time, as the swing of the pendulum is regular and can be used to keep track of the passing of time. Pendulums are also used in clocks, swinging back and forth to mark the seconds and minutes. In addition to clocks, pendulums are also used in scientific experiments, such as determining the acceleration due to gravity. The length of the pendulum and the period of its swing are related, with a longer pendulum having a longer period. Pendulums can be used to measure the strength of a gravitational field, as the period of the pendulum is affected by the local strength of the gravity.
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a smooth wooden 40.0 n block is placed on a smooth wooden table. a force of 14.0 n is required to keep the block moving at constant velocity. what is the coefficient of sliding friction between the block and the table top? if a 20.0 n brick is placed on top of the wooden block, what force will be required to keep the block and brick moving at constant velocity?
The coefficient of sliding friction between the block and the table top is 0.35. The force will be required to keep the block and brick moving at constant velocity is 21 N.
The coefficient of sliding friction (μ_s) is given by the ratio of the force of friction to the normal force.
For the wooden block on the table top:
Fs = μs * N
where
Fs = 14.0 N (force required to keep the block moving at constant velocity)
N = 40.0 N (normal force on the block)
So
μs = Fs / N = 14.0 N / 40.0 N = 0.35
When a 20.0 N brick is placed on top of the wooden block, the normal force on the block increases to 60.0 N (40.0 N + 20.0 N).
The force required to keep the block and brick moving at constant velocity can be calculated using the same formula as above:
Fs = μs * N
where
N = 60.0 N (new normal force)
so
Fs = μs * 60.0 N = 0.35 * 60.0 N = 21.0 N
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the air in an inflated balloon (defined as a system of government) is warmed over a toaster and absorbs 125 j id heat. as ir does 79 kj of work. what is the change in internal energy for the system
The change in internal energy of the air in the inflated balloon (defined as the governing system) is heated over a toaster and absorbs 125J of heat. As it expands, it does 78 kJ of work = - 78,875 J
Energy cannot be generated or destroyed; instead, it can only be transformed from one form to another, according to the basic law of thermodynamics.
The formula:
ΔE = q + w
ΔE = the internal energy (J)
q = heat added/taken away (J)
w = the system's or its own work (J)
The system absorbed heat since it was already warm, so:
q = positive.
It worked because the gas expanded, so:
w = negative.
ΔE = q + w
= 125 J + (-79 x 10³ J)
= - 78,875 J
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A 3.0 nc charge at x-0 cm and a -1.o nc charge is at x-4 cm. At what point or points on the x-axis is the electric potential zero?
At -6cm from small charge on the x-axis is the electric potential zero.
What is electric potential?Electric potential is the effort required to move a unit charge from one point to another while battling an electric field. Though any location outside the range of the electric field charge can be used, Earth is typically used as the reference point.
The diagram depicts the forces acting on a positive charge (q) that is situated between two plates (A and B) of an electric field (E). To move the charge from plate A to plate B, an equal and opposite force (F′ = qE) must be applied because the electric force F exerted by the field on the positive charge is F = qE. The work W required to move the positive charge over a distance d is W = F′d = qEd.
Two unlike charges are separated by a distance d two zero potentials points are obtained one between the charges(x)
and other out side nearer the small charge(y)
here
x = d/((q2/q1)+1)
And
d = 4cm,
q1 = 3,
q2 = -1
x=4/(1/3)+1=3cm
y=d(/q2/q1)-1)
then
y = 4/(1/3)-1
= -6cm from small charge
Thus, at -6cm from small charge on the x-axis is the electric potential zero.
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soccer fields vary in size. a large soccer field is 115 m long and 85 m wide. what are its dimensions in feet and inches?
Length in feet and inches:: 378 feet 6 inches
Width in feet and inches: : 279 feet 2 inches
what is dimensions?Dimensions are the measurement of something's size, such as length, width, and height. Dimensions can be used to describe the overall size of an object, or more specifically, its components.
They can also be used to quantify the area or volume of an object. Dimensions are usually expressed in metric units such as centimeters, meters, or millimeters, although imperial units are also used.
Calculation:
Length: 115 m x 3.28 ft/m = 378.8 ft ≈ 378 ft 6 inches
Width: 85 m x 3.28 ft/m = 279.2 ft ≈ 279 ft 2 inches
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Burning fossil fuels does not substantially impact the amount of carbon in
the atmosphere over time.
O True
O False
Answer: False.
Explanation:
Over the last century, burning of fossil fuels like coal and oil has increased the concentration of atmospheric carbon dioxide (CO2). This increase happens because the coal or oil burning process combines carbon with oxygen in the air to make CO2.
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Two runners start at the same point and jog at a constant speed along a straight path. runner a starts at
time t = 0s, and runner b starts at time t = 2.5 s. the runners both reach a distance 64 m from the starting
point at time t = 25 s.
if the runners continue at the same speeds, how far from the starting point will each be at time t = 45 s?
options:
runner a's distance will be 115.2 m, and runner b's distance will be 120.7 m.
o runner a's distance will be 64 m, and runner b's distance will be 71 m.
o runner a's distance will be 115.2 m, and runner b's distance will be 133.65 m.
runner a's distance will be 64 m, and runner b's distance will be 133.65 m
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A) runner a's distance will be 115.2 m, and runner b's distance will be 120.7 m.
What is distance?Distance is a numerical measurement of how far apart two objects or points are from one another. Distance can be measured in a variety of ways including miles, kilometers, feet, and meters.
To solve this problem, we need to use the equation d = rt, where d is the distance, r is the rate, and t is the time. Since both runners are running at a constant speed, we can assume the rate (r) is the same for both.
We can calculate the rate by using the information that both runners were 64 m away from the starting point after 25 s. We can plug this information into the equation to get:
64 m = r * 25 s
Solving for r, we get:
r = 2.56 m/s
Now that we have the rate, we can plug it into the equation to calculate the distances for both runners at time t = 45 s.
For runner a (who started at t = 0s), the distance will be:
d = 2.56 m/s * 45 s
d = 115.2 m
For runner b (who started at t = 2.5 s), the distance will be:
d = 2.56 m/s * 42.5 s
d = 120.7 m
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A sinusoidal wave of frequency 500 Hz has a speed of 350 m/s. (a How far apart are two points that differ in phase by pi/3 rad? (b) What is the phase difference between two displacements at a certain point at times 1.00 ms apart?
(a) To find the distance between two points that differ in phase by π/3 radians, we can use the wavelength of the wave, which is given by the speed of the wave divided by the frequency:
Wavelength = Speed of wave / Frequency
Given that the frequency is 500 Hz, the wavelength is:
Wavelength = 350 m/s / 500 Hz = 0.7 m
The phase difference between the two points is equal to the difference in the phase of the wave at these points. The phase difference in radians is given by the product of the wave number and the distance between the points.
The wave number is equal to 2pi/wavelength, so:
k = 2π / wavelength = 2*π / 0.7 m = 8.6 rad/m
The distance between the two points that differ in phase by pi/3 rad is given by:
Distance = π/3 / k = π/3 / 8.6 rad/m = 0.035 m
(b) To find the phase difference between two displacements at a certain point at times 1.00 ms apart, we can use the angular frequency of the wave, which is given by the product of 2π and the frequency:
ω = 2π * frequency = 2π * 500 Hz = 3141.59 rad/s
The phase difference between two displacements at a certain point at times 1.00 ms apart is given by the product of the angular frequency and the time interval.
Given that the time interval is 1.00 ms = 0.001 s, the phase difference is:
Δφ = ω * time interval = 3141.59 rad/s * 0.001 s = 3.14 rad
Therefore, the phase difference between two displacements at a certain point at times 1.00 ms apart is 3.14 rad.
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