The correct mathematical relationship for the two times is Option B: TE = √gM/gE . TM.
What is gravity?Gravity is a natural phenomenon that causes objects with mass to be attracted to one another. It is one of the four fundamental forces in nature and is responsible for the formation and structure of galaxies, stars, and planets. Gravity is experienced as a force pulling objects towards each other. The strength of gravity depends on the distance between two objects, as well as their masses.
This is because the acceleration due to gravity is inversely proportional to the time taken for an object to fall. The equation for this is:
Time = √2*Distance/Acceleration.
Therefore, if we substitute the values for the Moon and Earth in this equation, we get:
TE = √gM/gE . TM
where gM and gE are the accelerations due to gravity on the Moon and Earth, respectively, and TM and TE are the times taken for the object to reach the Moon's and Earth's surfaces, respectively.
To learn more about gravity
https://brainly.com/question/2537310
#SPJ4
A 3. 1-kilogram gun initially at rest is free to move. When a 0. 015-kilogram bullet leaves the gun with a speed of 500 meters per second, what is the speed of the gun?.
The speed of the gun which was initially at rest and leaves the bullet with certain speed is calculated to be 2.42 m/s.
Given that,
Mass of the gun M = 3.1 kg
The bullet's mass is m = 0.015 kg
The bullet's speed is v = 500 m/s
According to momentum conservation principle, the momentum before the bullet leaving the gun is equal to the momentum after the bullet leaving the gun. Both the gun and the bullet will be at rest initially, so the total momentum must be equated to zero.
Mathematically, 0 = m v + M V
where,
V is the velocity of the gun
Making V as subject, we have,
V = - (m v)/ M = -(0.015 × 500)/3.1 = -2.42 m/s
Hence, the gun is moving 2.42 m/s faster than the bullet.
To know more about speeds:
https://brainly.com/question/864795
#SPJ4
Anna holds a 14 D magnifier directly in front of her eye to get a close look at a 19-mm -diameter penny. Assume a typical 25 cm near point and a distance of 1.7 cm between the lens and the retina.
What is the closest possible distance that she can hold the coin to have it appear in focus?
Express your answer with the appropriate units.
The closest possible distance that she can hold the coin to have it appear in focus is 5.44 cm.
Given:
Magnifier lens power = 14 D
Near point = 25 cm
Distance between lens and retina = 1.7 cm
Diameter of the penny = 19 mm
The focal length is:
f = 1÷D
f = 1 ÷ 14 = 7.1 cm
The image distance is:
v = -(near point - Distance between lens and retina)
v = - (25 - 1.7)
v = - 23.3 cm
From lens formulae:
1/f = 1/u + 1/v
u = vf/(v-f)
u = -23.3×7.1÷(-23.3 - 7.1)
u = 5.44 cm
Hence, the closest possible distance that she can hold the coin to have it appear in focus is 5.44 cm.
To learn more about Distance, here:
https://brainly.com/question/13034462
#SPJ12
g when a helium balloon rises it gains ke and gravitational pe. where does that energy come from?
Kinetic energy comes from the motion of the helium balloon, and gravitational potential energy comes from the relative position of the balloon with respect to the ground surface.
Kinetic energy is defined as the energy which an object possessed due to the virtue of its motion. It is equal to the product of mass of the object and square of the velocity.
On the other hand, gravitational potential energy is defined as the energy which is possessed by the object due to position or configuration related to the other objects. If an object of mass m, is situated at a height of h, then its gravitational potential energy will be, p = mgh.
To know more about Kinetic energy, here
https://brainly.com/question/26472013
#SPJ4
if your brakes fail, the first thing to do is to... choose one a. apply the parking brake. b. shift to a lower gear, then apply the parking brake. c. pump your brakes. d. shift to neutral.
Answer:
apply the parking break
two masses have the same linear momentum. one mass is 3 kg and the other is 4 kg. which mass has greater kinetic energy?
The mass with greater kinetic energy is the 4 kg mass.
What is mass?Mass is a measure of the amount of matter in a given object. It is usually measured in kilograms (kg) or grams (g). 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, which means it doesn't change depending on where it is located.
Kinetic energy is calculated using the equation KE = 1/2mv2, where m is the mass and v is the velocity. Since the two masses have the same linear momentum, then the velocity of the 4 kg mass must be greater than the velocity of the 3 kg mass. This means that the 4 kg mass has a greater kinetic energy because it has a greater mass and a greater velocity. Therefore, the 4 kg mass has a greater kinetic energy.
To know more about mass click-
https://brainly.com/question/19385703
#SPJ4
two masses have the same linear momentum. one mass is 3 kg and the other is 4 kg. The mass with greater kinetic energy is the 4 kg mass.
What is mass?Mass is a measure of the amount of matter in a given object. It is usually measured in kilograms (kg) or grams (g). 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, which means it doesn't change depending on where it is located.
Kinetic energy is calculated using the equation
K.E. = 1/2mv²,
where m is the mass and
v is the velocity.
Since the two masses have the same linear momentum, then the velocity of the 4 kg mass must be greater than the velocity of the 3 kg mass.
This means that the 4 kg mass has a greater kinetic energy because it has a greater mass and a greater velocity.
Therefore, the 4 kg mass has a greater kinetic energy.
To know more about mass refer to-
brainly.com/question/19385703
#SPJ4
This problem explores the behavior of charge on conductors. We take as an example a long conducting rod suspended by insulating strings. Assume that the rod is initially electrically neutral. For convenience we will refer to the left end of the rod as end A, and the right end of the rod as end B.
The charge of the same sign will repel as the ball with a negative charge moves toward the A end of the neutral bar, and when they do so, they move to the left end, leaving the rod with a positive charge.
What do you mean by charge?
Charge, also known as electric charge, electrical charge, or electrostatic charge and denoted by the symbol q, is a property of a unit of matter that indicates how many more or fewer electrons than protons it contains.
What does the term "charge" in chemistry mean?
Subatomic particles have a characteristic known as "electric charge" that makes them experience force while in an electric and magnetic field. Positive and negative charges are the two forms of electricity that are often carried by.
To know more about charge visit:
https://brainly.com/question/25939248
#SPJ4
a person is hanging motionless from a vertical rope over a swimming pool. she lets go of the rope drops straight down. after letting go, is it possible for her to curl into a ball and start spinning? justify your answer.
It is possible for the person to curl into a ball and start spinning after letting go of the rope. However, it would require some effort to initiate the spinning motion.
What do you mean by motion?An object changing its position with respect to time is referred to as motion. Motion is mathematically described in terms of displacement, distance, velocity, acceleration, and speed.
As the person is falling, the only force acting on her body is gravity pulling her downward. Therefore, there is no horizontal force acting on her body to cause it to spin. However, if the person were to curl into a ball and then actively start spinning by twisting her body or flailing her arms, she could create a torque, which is a force that causes rotation.
It's worth noting that the spinning motion would not have a significant effect on the person's trajectory of falling into the swimming pool, as air resistance is negligible compared to her weight, and the spinning motion would be quickly dampened by the drag caused by the water resistance.
To know more about motion, visit:
brainly.com/question/22810476
#SPJ4
Find the output force exerted by a moveable pulley if the input force is 50 N.
Please give the equation.
Answer:
Because the mechanical advatage of a movable pulley is always two you multipy the input force times two. So 50 * 2 = 100N
a 250 g ball travels at a velocity of 40 m/s. its momentum is O 160 kg-m/s. O 10 kg-m/s. O 4 kg.m/s. O 10,000 kg·m/s
When a 250 g ball travels at a velocity of 40 m/s, its momentum is 10 kg-m/s.
In physics, momentum is defined as the product of an object's mass and velocity. It is a vector quantity, which means it has both magnitude and direction. The direction of momentum is the same as the direction of motion of the object.
The momentum of an object is equal to its mass multiplied by its velocity. Therefore, the momentum of a 250 g ball traveling at a velocity of 40 m/s is:
momentum = mass x velocity
momentum = 250 g x 40 m/s
momentum = 10,000 g-m/s
Note that the unit of momentum is usually represented as kgm/s, but since the mass is given in grams, we need to convert it to kg.
momentum = 10,000 gm/s = 10 kg-m/s
Learn more about momentum here: https://brainly.com/question/7538238
#SPJ4
if a thin thread is placed between a screen and a bright source of light, a pattern of parallel dark and bright fringes appears on the screen. the phenomenon best explaining the formation of this pattern is:
If a thin thread is placed between a screen and a bright source of light, a pattern of of parallel light and dark strips appears on the screen. This phenomenon is called the diffraction of light.
When a thin thread comes in the path of light waves, it obstructs the upfront of the light wave causing the change in the phase difference of the wave. Overlapping of these different waves of different phase differences cause the dark and light pattern appearance on the wall. On the other hand, thin thread also cast a thin shadow due to the obstruction in the path of light. Pattern on the wall depends on the phase difference in the wave-upfront.
To know more about diffraction, here
https://brainly.com/question/12290582
#SPJ4
While riding a bike, you convert chemical energy into kinetic energy. After pedaling for a certain time you have given yourself and the bike (a combined mass of 78 kg) a kinetic energy of 9,011 Joules. How fast are you going at that moment in m/s?
According to the question of kinetic energy, 15.4m/s fast you are going at that moment in m/s.
What is kinetic energy?
Kinetic energy is a form of energy that is associated with the motion of an object. It is the energy an object has due to its motion. Kinetic energy is present in all moving objects and is calculated by taking the mass of the object and multiplying it by the square of its velocity. Kinetic energy is a form of energy that can be transformed into other forms. For example, when a ball is dropped and bounces off the ground, it converts its kinetic energy into potential energy. Similarly, when an object is moving and then comes to a stop, its kinetic energy is converted into heat energy.
The kinetic energy can be calculated by the equation KE = 1/2mv2.
Therefore, v = √(2KE/m) = √(2*9011/78) = 15.4 m/s.
To learn more about kinetic energy
https://brainly.com/question/20658056
#SPJ1
Find the ratio of the volume divided by the temperature for the first data pair. Use significant figures.
V / T = 0.72/276 =
The volume to temperature conversion factor for the first set of data. Use meaningful numbers.
V / T = 0.72/276 = 0.0026
What is temperature ?The average temperature energy produced by a system is measured as temperature, which is a crucial physical characteristic that influences how matter behaves. A thermometer is used to measure temperature, usually in the Celsius & Fahrenheit scales. Temperature is often related to the kinetic energy of the objects that compose up an object and can be thought as the "hotness" / "coldness" of an object. Numerous variables, including the energy of the environment, a material's thermal conductivity, or the amount of heat absorbed or released during a chemical or nuclear event, influence temperature.
To learn more about temperature
https://brainly.com/question/26866637
#SPJ4
Answer:
V / T = 0.72/276 = 0.0026
Explanation:
State the law of conservation of linear momentum and describe its consequences.
The law of conservation of linear momentum states that the total momentum of a system is always conserved and the consequence is that the system must be isolated.
What is the law of conservation of linear momentum?The law of conservation of linear momentum states that in an Isolated system, the total momentum of the system is always conserved.
Mathematically, the formula for the conservation of linear momentum is given as;
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
where;
m₁ is the mass of the first objectm₂ is the mass of the second objectu₁ is the initial speed of the first objectu₂ is the initial speed of the second objectv₁ is the final speed of the first object v₂ is the final speed of the second objectBased on the law of the conservation of linear momentum, the sum of the initial momentum of the system will be equal to the sum of the final momentum of the system provided the system is isolated.
Thus, the consequences of conservation of linear momentum is that the total momentum of the system will not be conserved if the system is not isolated.
Learn more about conservation of linear momentum here: https://brainly.com/question/7538238
#SPJ1
a 90.0-kg fullback running east with a speed of 5.00 m/s w is tackled by a 95.0-kg opponent running north with a q/c speed of 3.00 m/s. (a) explain why the successful tackle
The speed of the players just after the successful tackle is 2.9 m/s.
In physics, what is a momentum?The amount of motion a body has is referred to as its momentum. Given that momentum depends on both velocity and the direction of the body's motion, it is quantified as "mass velocity". Because velocity is a vector, momentum is a vector quantity, whereas mass is a scalar quantity. Mass times speed equals momentum.
Ф = tan^-1 (m2 u2/m1u1) = 32.3
m1 u1 = (m1 + m2) v cosФ
v => m1u1/ (m1+m2) x cosФ
=> 90 x 5/(90+95) cos 32.3
=> 2.9 m/s.
What is the explanation for the law of conservation of momentum?The momentum conservation law says as much. Except for the application of an external force, the total momentum of two or more bodies operating on one another in an isolated system is constant. Determining momentum is impossible since it cannot be done.
Learn more about speed here:
brainly.com/question/28336182
#SPJ4
what is the magnitude of a point charge that would create an electric field of 2.10 n/c at points 3.40 m away?
At a distance of 3.40 m from the source, the electric field's strength is calculated to be 1.111010C.
How big of a point charge would be needed to produce an electric field?
Test = k | Q | r 2 when E = F q. The size of the electric field produced by a point charge Q is determined by this equation. The distance r in the denominator is the separation between the point of interest and the point charge, Q, or the center of a spherical charge.
What is the magnitude field formula?
The equation describes the force acting on a wire carrying current I and having length L in a magnetic field. Where is the angle formed by the wire and the magnetic field, and F=ILBsin.
To know more about electric field visit:
brainly.com/question/15800304
#SPJ4
we measured the orbital period of a planet orbiting a star exactly like our sun, to be 2 hours. where is such a star located? answer in units of au.
According to Kepler's Third Law, the cubes of the quasi axes of the orbits of planets are directly related to the squares of the planets' orbital periods. The Third Law of Kepler suggests that
What is a ratio?
proportionate definition (End of Entry 2) 1a: equal in size, extent, or intensity. B: Corresponding sides of identical triangles are proportionate if their ratios are the same or constant. A proportionate system of migration quota regulates or determines in size or extent with regard to proportions.
What is proportion's polar opposite?
Phrases equivalent to the word proportionate. Similar words for proportionate. Asymmetry, distortion, irregularity, lopsidedness, nonsymmetry,
To know more about proportional visit:
https://brainly.com/question/3254974
#SPJ4
As the frequency of a wave increases on the electromagnetic spectrum, what happens to the wave's energy
As the frequency of a wave increases on the electromagnetic spectrum, the wave's energy increases.
What is electromagnetic spectrum?The electromagnetic spectrum is a term used to describe the entire range of frequencies of electromagnetic radiation, from the longest wavelength radio waves to the shortest wavelength gamma rays. It is composed of various types of electromagnetic radiation, including radio waves, microwaves, infrared, visible light, ultraviolet, x-rays and gamma rays. Electromagnetic radiation can travel through space and can be absorbed, reflected, or refracted by various objects. Electromagnetic radiation is used in various fields such as communications, astronomy, medicine, and industry. For example, radio waves are used for communication, microwaves are used for cooking food, infrared radiation is used for medical imaging, visible light is used for sight, ultraviolet radiation is used for disinfection, x-rays are used for medical imaging and gamma rays are used for cancer treatment. Electromagnetic radiation has both electric and magnetic fields that are perpendicular to each other and to the direction of propagation.
To learn more about electromagnetic spectrum
https://brainly.com/question/2261239
#SPJ4
if you were asked to determine the 3-dimensional shape of a specimen, which objective lens would you use? explain your reasoning in complete sentences.
The objective lens used to determine the 3-dimensional shape of a specimen would depend on the type of imaging technique being used.
What is objective lens ?In general, the objective lens used would be one that is capable of providing high resolution and high contrast images in order to clearly distinguish the different features and structures of the specimen. Additionally, the objective lens should be matched to the type of imaging technique being used, as different techniques have different requirements for resolution, contrast, and depth of field.
For example, if using a scanning electron microscope (SEM), a high-resolution, high-magnification objective lens would be used to capture detailed images of the specimen's surface. On the other hand, if using a confocal laser scanning microscope (CLSM), a high numerical aperture (NA) objective lens would be used to capture images of the specimen in 3D by selectively illuminating and detecting fluorescence from specific depths within the specimen.
To know more about objective lens visit:
https://brainly.com/question/3174756
#SPJ4
when connecting manifold gauges to a heat pump that is in heating mode the hoses should be connected to the?
The hoses should always be hooked to that same vacuum pump when installing manifold gauges on a heat engine that is operating in the heating mode.
What do people's gauges represent?When alluding to the jewellery itself, the phrase "gauge" is really just a made-up byword for "stretched earlobes." Gauges are sometimes referred to as jewellery by those who are unfamiliar with the technical jargon used in body modification. The width of piercings once they reach an inch is known as the gauge.
What does gauge mean?The French term "jauge," which means "result of measuring," is the ancestor of the noun "gauge" and is tied to it. Documents as from 13th century make reference to this word.
To know more about Guages visit:
https://brainly.com/question/28087119
#SPJ4
Please help me thank you!
The row in the chart that correctly shows the system A, B, C is row 3, gas exchange, nutrients and waste removal.
option C is the correct answer.
What is Digestive system?The digestive system involves in the break down of food into simpler substances in which the body can absorb in form o nutrient.
The absorption of digested food or nutrient takes place in the small intestine found below the stomach.
The respiratory system involves the intake of oxygen for respiration and the removal of carbon dioxide out of the body. This system involves gas exchange in and out of the body.
The circulatory system transports oxygen, digested food ( nutrients ), water and waste materials around the body.
The waste material like urine is removed from the body through the urinary tract.
Thus, we can conclude that the first system given is for gas exchange, the second system given is for nutrient absorption, and the third system given is for removal of waste materials.
Learn more about digestive system here: https://brainly.com/question/956634
#SPJ1
TRUE OR FALSE As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward. Group of answer choices
As a projectile rises towards the peak of its trajectory, the vertical acceleration is directed upward; as it falls from the peak of its trajectory, its vertical acceleration is directed downward. The correct answer is TRUE.
As a projectile is launched into the air, it initially experiences an upward acceleration due to the force applied to it. This acceleration causes the projectile to move upwards, until it reaches the peak of its trajectory. At the peak, the projectile's velocity in the vertical direction is zero and the acceleration is directed downward due to the force of gravity.
As the projectile falls back towards the ground, it experiences a downward acceleration, causing its velocity in the vertical direction to become negative. This acceleration continues until the projectile lands on the ground.
To learn more about trajectory visit: https://brainly.com/question/88554
#SPJ4
A small polyester ball and a piece of polyvinyl chloride (PVC) pipe are given the same negative charge. The ball is then placed over the PVC pipe, where it is observed to remain at rest 40 cm from the pipe. The mass of the polyester ball is 3.0 grams. Determine the charge on the ball.
The charge is ___uc
Also, solve with significant figures.
What do you think are the factors that might affect the magnitude of this angle
The bond angle in a compound is the angle formed between two bonds in the compound. It is affected by the geometry, electron cloud and the size of atoms.
What is bond angle ?Bond angle is the distance between two chemical bonds in a compound. Bond angle is affected by the electrostatic force of repulsion and attraction. Hence, the presence of lone pairs and bond pair are the main factors affecting the bond angle.
If there are lone pairs, the repulsion between two lone pairs is greater than that between a lone pair and bond pair which in turn greater than that between two bond pairs.
Hence, the electron clouds will align themselves to minimize the repulsion. Thus, the geometry and bond angle may vary from what we predicted based on hybridization.
Find more on bond angle:
http://brainly.com/question/13751116
#SPJ1
Your question is incomplete. But your complete question probably was:
What is bond angle? What do you think are the factors that might affect the magnitude of this angle?
A 3.7 kg block of wood sits on a frictionless table. A 3.0 g bullet, fired horizontally at a speed of 450 m/s , goes completely through the block, emerging at a speed of 230 m/s .What is the speed of the block immediately after the bullet exits?
The speed of the block immediately after the billet exist is 0.346m/s.
Describe speed.An object's speed is how quickly it moves through space. When moving quickly, an object can cover a large distance in a short period of time. As opposed to this, a slow-moving object travels a relatively short distance in the same amount of time. A thing that isn't moving at all is said to have zero speed.
Mass of wood = 3.7kg
Initial speed u₁=0
Mass of bullet is = 3x10⁻³kg
Initial speed of block =450m/s
Final speed of block v₂=230m/s
According to linear momentum
Initial linear momentum = Final linear momentum
Mu₁+mu₂ =Mv₁+ mv₂
Mx0 + 3x10⁻³ x450 = 3.7v₁ + 3x 10⁻³ x230
1.35-0.069 = 3.7v₁
1.281 = 3.7v₁
v₁ = 0.346m/s
The speed of the block immediately after the billet exist is 0.346m/s.
To know more about speed visit:
https://brainly.com/question/29063489
#SPJ4
In an RLC series circuit, which of the following does the quality factor of the circuit depend on? (Select all that apply.)
- Width of the resonance
- L
- R
- C
L
R
C...
On the values of the inductance (L), resistance (R), and capacitance (C). The L, R, and C values determine the resonance frequency of the circuit.
What is the Quality Factor(Q) of an RLC Circuit?The quality factor (Q) of an RLC series circuit is a measure of how underdamped the circuit is. It is defined as the ratio of energy stored in the circuit to energy lost per cycle. In an RLC series circuit, the Q factor depends on the values of the inductance (L), resistance (R), and capacitance (C). The L, R, and C values determine the resonance frequency of the circuit, as well as the damping of the oscillations at that frequency.
The value of L determines the amount of energy stored in the circuit's magnetic field. A higher value of L results in a higher Q factor.
The value of R determines the amount of energy lost in the circuit due to resistance. A lower value of R results in a higher Q factor.
The value of C determines the amount of energy stored in the circuit's electric field. A higher value of C results in a higher Q factor.
The width of the resonance, which is the difference between the frequency at which the circuit is resonant and the frequency at which the circuit's impedance is half the resonant impedance is also dependent on the Q factor, as the Q factor is inversely proportional to the width of the resonance.
To know more about resonance visit: https://brainly.com/question/15337338
#SPJ4
The spelling of occasion
Answer:
occasion - a particular event, or the time at which it takes place.
Determine the total heat transfer for the reversible process 1-2 shown in the given figure. T1 is 100°C T2 is 600°C. С Т. 100 0.2 1.0 S, kJ/K The total heat transfer for the reversible process 1-2 is D k J.
The reversible process 1-2's overall heat transfer is [tex]Q_{1-2}[/tex] =482.4 KJ
Heat transfer is a subfield of thermal engineering that focuses on the production, use, conversion, and exchange of thermal energy across physical systems. Thermal conduction, thermal convection, thermal radiation, and energy transfer through phase changes are some of the different types of heat transfer processes that are characterized. Heat transfer is a subfield of thermal engineering that focuses on the production, use, conversion, and exchange of thermal energy across physical systems. Thermal conduction, thermal convection, thermal radiation, and energy transfer through phase changes are some of the different types of heat transfer processes that are characterized.
[tex]Q_{1-2} =[/tex]Area under curve 1-2 on
[tex]Q_{1-2} =\frac{1}{2}[/tex]x0.8x(833.373) + 0.8x373
[tex]Q_{1-2} =[/tex]184+298.4
[tex]Q_{1-2} =\\[/tex]482.4KJ
Question)- Determine The Total Heat Transfer For The Reversible Process 1-2 Shown In The Given Figure. T1 Is 100°C T2 Is 600°C. С Т. 100 0.2 1.0 S, KJ/K The Total Heat Transfer For The Reversible Process 1-2 Is D K J.Learn more about heat transfer
brainly.com/question/13433948
#SPJ4
An experiment is performed to test the effects of sleep deprivation on rote memory. In this experiment, the dependent variable is thea. number of hours subjects go without sleep.
b. rote memory scores.
c. number of subjects deprived of sleep in the experimental group.
d. correlation between hours of sleep and fatigue.
In this experiment, the main focus is to test the effects of sleep deprivation on rote memory. Thus option B is the correct answer.
The dependent variable in this experiment is the rote memory scores of the subjects.
Rote memory is the ability to memorize information through repetition, and this is the outcome that the experimenters are trying to measure and observe changes in. The independent variable in this experiment is the number of hours that the subjects go without sleep. This variable is manipulated by the experimenter to induce sleep deprivation in the subjects, and the effects of this manipulation on the dependent variable (rote memory scores) are studied.
The number of subjects deprived of sleep in the experimental group and the correlation between hours of sleep and fatigue are also important factors to consider in the experiment, but they are not dependent variables.
To learn more about Sleep deprivation,
https://brainly.com/question/17583335
#SPJ4
how much force is required to keep a 4-kg object moving to the right with a constant speed of 8.0 m/s?
According to the Newton’s first law of motion, any object will remain in its condition of motion unless an unbalanced force acts upon it. Therefore, 0 net force is required to keep a 4 kilogram object's moving to the right at a constant speed of 8.0 m/s.
Newton's first law of motion states that an item does not require a force to remain in motion. Only a net force is required to affect the velocity of an object. The 4 kilograms object is moving at a constant velocity, it means the acceleration will be 0. Hence, there is no net force acting on it (0 Newtons).
To learn more about Newton’s first law of motion, click here:
https://brainly.com/question/26108169
#SPJ4
Problem 4.8 A particle's trajectory is described by x =(12t3−2t2)m and y =(12t2−2t)m, where t is in s.
Part A What is the particle's speed at t=0s ? v = m/s
Part B What is the particle's speed at t=5.0s ? Express your answer using two significant figures. v = m/s
Part C What is the particle's direction of motion, measured as an angle from the x-axis, at t=0 s ? Express your answer using two significant figures. θ =
Part D What is the particle's direction of motion, measured as an angle from the x-axis, at t=5.0s ? Express your answer using two significant figures. θ =
A. The particle's speed at t = 0 s is 2m/s.
B. The particle's speed at t=5.0s is 38.2 m/s.
C. The particle's direction of motion, measured as an angle from the x-axis, at t=0 s cannot be defined.
D. The particle's direction of motion at t = 5.0 s is 64.9 degrees.
What is velocity vector?A velocity vector represents the rate of change of the position of an object. The magnitude of a velocity vector gives the speed of an object while the vector direction gives its direction. Velocity vectors can be added or subtracted according to the principles of vector addition.
Part A: To find the particle's speed at t = 0 s, we need to find the magnitude of its velocity vector. The velocity vector is given by the derivative of the position vector with respect to time. So: v = [tex]\sqrt{( (dx/dt)² + (dy/dt)² )}[/tex]
dx/dt = 36t² - 4t, dy/dt = 24t - 2
Therefore, at t = 0 s: v = [tex]\sqrt{(360^2 - 40)^2 + (24*0 - 2)^2 )}[/tex] = [tex]\sqrt{4}[/tex] = 2 m/s
Part B: To find the particle's speed at t = 5.0 s, we substitute t = 5.0 s into the equation for v: v = [tex]\sqrt{(365.0^2 - 45.0)^2 + (24*5.0 - 2)^2 ) }[/tex]= [tex]\sqrt{(1444)}[/tex] ≈ 38.2 m/s.
Part C: To find the direction of motion, we need to find the angle the velocity vector makes with the positive x-axis. We can use the arctangent function to find this angle: θ = atan(dy/dt / dx/dt)
Therefore, at t = 0 s: θ = atan( (240 - 2) / (360² - 4×0) ) = atan(-2/0) = undefined
Part D: To find the particle's direction of motion at t = 5.0 s, we substitute t = 5.0 s into the equation for θ: θ = atan( (245.0 - 2) / (365.0² - 4×5.0) ) ≈ 64.9 degrees
Note: The answer is given in degrees, if you want it in radians you can use the conversion formula rad = (pi/180)degree.
To know more about speed, visit:
https://brainly.com/question/28224010
#SPJ4
