The mass of the mouse, m₁=0.042 kg
The mass of the 1st cart, m₂=0.35 kg
The mass of the second cart, m₃=0.25 kg
The speed of the 1st car after the jump, u₁=0.88 m/s
From the law of conservation of momentum, the momentum of a system should always remain the same.
Before the mouse jumps from one cart to another, all the objects were at rest. Therefore the total momentum of the system was zero.
Thus after the mouse jumps, the total momentum of the system should be equal to zero.
Thus the momentum of the second cart and the mouse will be equal in magnitude to the momentum of the first cart but it will be in the opposite direction.
Thus,
[tex]m_2u_1=(m_1+m_3)v_2[/tex]On substituting the known values,
[tex]\begin{gathered} 0.35\times0.88=(0.042+0.25)v_2 \\ \Rightarrow v_2=\frac{0.35\times0.88}{(0.042+0.25)} \\ =1.05\text{ m/s} \end{gathered}[/tex]Thus the speed of the mouse and the second cart after the mouse jumps is 1.05 m/s
What average mechanical power (in W) must a 76.5 kg mountain climber generate to climb to the summit of a hill of height 305 m in 42.0 min? Note: Due to inefficiencies in converting chemical energy to mechanical energy, the amount calculated here is only a fraction of the power that must be produced by the climber's body.
Power is given by, P= W/t, where W is mechanical work done and t is time taken.
From work-energy relation, work done is equal to the change in potential or kinetic energy.
W = mg[tex]h_{2}[/tex] - mg[tex]h_{1}[/tex]
Given,
Mass of mountain climber, m =76.5kg
Height of mountain hill, [tex]h_{2}[/tex] = 305m
Time taken to climb, t = 42 min= 42×60s= 2520s.
Since climber starts from the down of hill, [tex]h_{1}[/tex] = 0m. So, [tex]h_{2} - h_{1}[/tex] = 305m.
Work done, W = 76.5kg × 9.8m/[tex]s^{2}[/tex] × 305m
⇒W = 22.866×[tex]10^{4}[/tex] J.
Average mechanical power, P = 22.866×[tex]10^{4}[/tex]J ÷ 2520s
⇒P = 90.7375 W (watt)
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Decreasing a telescope's eyepiece focal length will:
increase magnification
decrease magnification
have no effect on magnification
Decreasing a telescope's eyepiece focal length increases magnification.
What is Magnification?The degree to which a telescope magnifies its subject. It is equal to the focal length of the telescope divided by the focal length of the eyepiece.
By doing two things, a telescope makes celestial objects visible:
1) making very faint objects visible by collecting much more light than the human eye can by itself using a big lens or mirror.
2) enlarging the things' size to make it easier to perceive their features.
On decreasing the focal length of the eyepiece focal length the magnification will increase.
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How much gravitational force is acting on a 5 kg bowling ball resting on the floor?
A. 0.2 N
B. 9.8 N
C. 1 N
D. 49 N
Answer:
Explanation:
F = m * a = 5 kg * 9.81 m/s^2 = ~ 49 N
consider newton's 3rd law, the force that the earth exerts on a person will be equal and opposite that what the person applies to the earth. however, why don't we see the earth accelerate?
According to Newton's third law, for every action there is an equal and opposite reaction. However, the land we see on earth is stationary and the force applied by us is not at all sufficient to make a movement or to accelerate.
What is Newton's third law of motion ?According to Newton's third law, for every action there is an equal and opposite reaction. Therefore, when we apply a force on an object, the object will exerts an equal and opposite force.
According to Newton's second law of motion, the force exerted on a body is the product of mass and acceleration. Hence, the force acting on body is directly proportional to the mass of the body and it accelerates by the applied force.
The mass of humans in earth is negligible compared to the mass of earth . Therefore, the force we exert on earth is not at all sufficient to accelerate the earth. However, earth in turn exerts an equal and opposite force.
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A jet taxiing down the runway receives word that it must return to the gate. The jet is traveling 43. 0 m/s when the pilot receives the message. What is the acceleration of the plane if it takes the pilot 7. 69 s to bring the plane to a halt?
The acceleration of the plane is: -5.59 m/s²
The formula for uniformly varied rectilinear motion (UVRM) and procedure that we will use to solve this exercise is:
a = (vf - vi) /t
Where:
vf = final velocityvi = initial velocitya = accelerationt= timeInformation about the problem:
vi = 43.0 m/svf= 0 m/st = 7.69 sa = ?Applying the acceleration formula we have:
a = (vf - vi) /t
a = (0 m/s - 43.0 m/s) /7.69 s
a = (-43.0 m/s) /7.69 s
a = -5.59 m/s²
What is acceleration?It is a physical quantity that indicates the variation of velocity as a function of time, it is expressed in units of distance per time squared e.g.: m/sec2 ; km/h2
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PLEASE ANSWER ASAP!
On average, there is enough wind in the UK each year to supply all of the UK's electricity needs.
Explain why the UK may still need power stations that use fuel to generate electricity.
(2 marks)
Explanation:
Unplanned maintenance at nuclear plants and lower than average wind speeds mean the country is currently relying on gas-powered stations to generate about half its electricity
The UK depends on power stations due to the more efficiency of energy production in them.
Even though UK has an enough wind supply over each year to meet the electric needs of UK, they still need power stations that use fuel to generate electricity.
This is because of the challenges created in the maintenance and implementation of wind plants in the UK.
The wind turbines have a higher cost for maintenance, compared to that of power stations. The ideal wind sites in the UK are mostly located in remote areas, so that it becomes more difficult for the implementation of wind plants. Also the lower average wind speed causes less production in the electricity through them. As a result, the UK still depends on power stations for the electric needs.
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Please help and explain will mark brainiest!!!
The particles or energy in a transverse wave travel up and down, perpendicular to the direction of the wave travel.
What is electromagnetic wave?
Electromagnetic waves are type of wave that do not require material medium for their propagation.
This type of waves travels in vacuum or in open medium.
Examples of electromagnetic waves include the follows;
Gamma raysx-raysultraviolet raysvisible lightinfra redmicro wavessound wavesElectromagnetic waves are known as transverse waves due to their mode of propagation.
In transverse wave, the particles of the medium travels perpendicular to their mode of vibration.
Thus, the particles or energy in a transverse wave travel up and down, perpendicular to the direction of the wave travel.
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PLEASE HELP ASAP!!! A high school athlete is in the weight room training for wrestling season. He is trying to bench press a bar loaded with 100
kg. How much force must he exert to lift the loaded bar and overcome the force of gravity?
Remember that a= 9.8 m/s² (1 point)
O 10.2 N
O 9800 N
O 980 N
109.8 N
Answer:
980N
Explanation:
100kg times 9.8m/s2
The force the high school athlete must exert to lift the loaded bar of mass 100 kg and overcome the force of gravity is 980 N
F = m a
F = Force
m = Mass
a = Acceleration
m = 100 kg
a = 9.8 m / s²
F = 100 * 9.8
F = 980 N
The equation used to solve the given problem is derived from the Newton's second law of motion. The law states that the force is the rate of change of momentum.
Therefore, the force the high school athlete must exert is 980 N
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in general, what is true about the frequency at which an object vibrates? multiple choice question. the slower the vibrations, the softer the sound the slower the vibrations, the higher the pitch the faster the vibrations, the louder the sound produced the faster the vibrations, the higher the pitch
The statement that is true concerning the frequency include the following: slower the vibrations, the softer the sound, the faster the vibrations, the louder the sound produced and the faster the vibrations, the higher the pitch. That is option A,C and D.
What is sound?Sound is defined as the type of wave that is being created when disturbance causes vibration through a medium such as water, air or solid medium.
The properties of a sound wave include the following:
Frequency,Pitch,Wavelength andAmplitude.The frequency of the sound wave is affects other properties which is the number of sound waves a sound produces per second.
A low frequency would lead to low sound and pitch production while a high frequency would lead to a high sound and pitch production.
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Mr. Mangan now sees a hoard of zombies running toward him. There are toomany for him to fight, so he makes a run for it. Starting from rest andaccelerating at a rate of 7 m/s2, he reaches a final velocity of 25 m/s. Howmuch time did it take for him to reach his final velocity?
Given data
*The given initial velocity is u = 0 m/s
*The given acceleration is a = 7 m/s^2
*The given final velocity is v = 25 m/s
The formula for the time taken to reach his final velocity is given by the kinematic equation of motion as
[tex]\begin{gathered} v=u+at \\ t=\frac{v-u}{a} \end{gathered}[/tex]Substitute the known values in the above expression as
[tex]\begin{gathered} t=\frac{25-0}{7} \\ =3.57\text{ s} \end{gathered}[/tex]Thus, the time taken to reach his final velocity is t = 3.57 s
you are given a 1/5 model of a car that normally runs at 30 mph. what wind tunnel speed should you use to test the car? (assume kinematic viscosity does not change and )
The wind tunnel speed that must be used to test the car 1 / 5 model of a car that normally runs at 30 mph is 150 mph
Re = u L / ν
Re = Reynold's number
u = Flow speed
L = Characteristic linear dimension
ν = Kinematic viscosity
ν[tex]_{p}[/tex] = 1.516 * [tex]10^{-5}[/tex] m² / s
ν[tex]_{p}[/tex] = ν[tex]_{m}[/tex] = 1.516 * [tex]10^{-5}[/tex] m² / s
L[tex]_{m}[/tex] = L[tex]_{p}[/tex] / 5
u[tex]_{p}[/tex] = 30 mph
Re[tex]_{m}[/tex] = u[tex]_{m}[/tex] L[tex]_{p}[/tex] / 5 * 1.516 * [tex]10^{-5}[/tex]
Re[tex]_{p}[/tex] = 30 L[tex]_{p}[/tex] / 1.516 * [tex]10^{-5}[/tex]
In tunnel,
Re[tex]_{m}[/tex] = Re[tex]_{p}[/tex]
u[tex]_{m}[/tex] L[tex]_{p}[/tex] / 5 * 1.516 * [tex]10^{-5}[/tex] = 30 L[tex]_{p}[/tex] / 5 * 1.516 * [tex]10^{-5}[/tex]
u[tex]_{m}[/tex] = 30 * 5
u[tex]_{m}[/tex] = 150 mph
Therefore, the wind tunnel speed that must be used to test the car is 150 mph
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if both the mass of a simple pendulum and its length are doubled, the period will if both the mass of a simple pendulum and its length are doubled, the period will increase by a factor of 0.71. increase by a factor of 2. be unchanged. increase by a factor of 4. increase by a factor of 1.4
The mass of the bob has no bearing on the pendulum's time period.The time duration would therefore remain the same if the mass of the bob doubled.
Solve the problem ?
The equation of motion for the pendulum can be found by using Newton's second rule for rotational systems: =ImgsinL=mL2d2dt2 and then rearranged as d2dt2+gLsin=0 d 2 d t 2 + g L sinIf the angular displacement's amplitude is sufficiently modest, the tiny angle... The length of the rope and the acceleration caused by gravity determine the time it takes for a simple pendulum to swing.When a simple pendulum's length is increased by four times, its period doublesWe currently have the simple pendulum era, which is the simple one to square root of and upon you.Now that the length has been extended, terrible food, we will have an easy quality to buy into L. A. Banjo's square root.This will be equivalent to dividing my by L squared and G by 4²That also is.Since the only factor in this situation is time, we will go into great detail.So, if the basic pendulum's length is raised by a factor of four, its time period will also double.That choice will be the right response. On Earth, a pendulum's swing is only greatly influenced by the length of its string.Students could question why a pendulum's period is solely determined by the length of the string.
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how do you find the average force applied for a wind-up toy car while it is speeding up? It speeds up for .8s and has a velocity of .741 m/s. Total motion is 220 cm over 2.70s. Converted the cm into m (100 cm = 1 M) any help?
The average force applied for a wind-up toy car while it is speeding up is 0.926m (N), where m is the mass of the toy.
What is the average force applied to an object?
The average force applied on an object is determined by applying Newton's second law of motion.
Mathematically, the average force applied on an object is given as;
F = ma
where;
m is the mass of the objecta is the acceleration of the objectThe acceleration of the wind up toy is calculated as follows;
a = v/t
where;
v is the velocity of the wind-up toyt is the time of motion of the toya = (0.741 m/s) / (0.8 s)
a = 0.926 m/s²
Substitute the value of the mass of the wind-up toy and its acceleration into the force equation to determine the average force applied to the toy.
F = m(0.926)
F = 0.926m (Newton)
Thus, the average force applied for a wind-up toy car while it is speeding up is 0.926m (N), where m is the mass of the toy.
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1.A 98.0 kg basketball player runs at a speed of 7.0 m/s. What is KE?
2.A jogger whose mass is 65 kg is moving at a speed of 4 m/s. What is the jogger's KE?
Answer:
Brainliest Answer?
2401J 520JExplanation:
E = ( 1 / 2 )mv²
b = ( 1 / 2 )( 98kg )( 7ms⁻¹ )²
b = ( 49 )²kgm²s⁻²
b = 2401J
j = ( 1 / 2 )( 65kg )( 4ms⁻¹ )²
j = ( 1 / 2 )( 65kg )( 16m²s⁻² )
j = 520kgm²s⁻²
j = 520J
Answer:
Explanation:
Given:
m = 98.0 kg
V = 7.0 m/s
__________
Ek - ?
KE - kinetic energy
Ek = m·V² / 2
Ek = 98.0*7.0² / 2 ≈ 2 400 J
An electrified rod attracts pieces of paper. After a while these pieces fly away! Why?
Answer: The paper prices fall off due to repulsive forces.
Explanation: When an electrified or charged object is brought near an uncharged object, it causes the electrons of the uncharged object to move as electrons are free movable particles. The electron leave behind the atoms. The uncharged object becomes ionized.
Here the pieces of paper may fall off because it becomes de-ionized by surrounding air particles. While the pieces are attached to the rod, surrounding air particles may provide or take away electrons and make the pieces become neutral again
Question
Draw the outlines of two cars, one
with a streamlined shape to reduce air
resistance, and one whose shape is not
streamlined. Explain why one may be
able to go faster than the other.
Because of this, race cars have streamlined bodies that enable them to go at significantly higher speeds.
Briefing:As there is less surface area to push the air against, the streamlined designed car will be able to cut through the air and produce less drag or resistance. They move slowly, as opposed to autos, which are not streamlined. Because of this, race cars have streamlined bodies that enable them to go at significantly higher speeds.
What is air resistance and how it can be reduced?In order to push against the force of the air, objects must be streamlined. Trains are made to move quickly between destinations because of their streamlined form. Even people, like swimmers, can attempt to be streamlined.
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How could these electronegativity values benefit you in analyzing data from the Curiosity rover?
It is to be noted that electronegativity will assist the analyst in the determination of the nature of the interactions between the elements discovered by the Curiosity Rover.
What is Electronegativity?The electronegativity values of two bound atoms indicate whether a bond is nonpolar or polar covalent, as determined by the bonding atoms' properties.
Electronegativity is a measurement of an atom's proclivity to attract electrons (or electron density) toward itself.
Electrons in a polar covalent bond are moved toward the more electronegative atom; consequently, the atom with the partial negative charge is the more electronegative atom. The bigger the electronegativity difference, the more polarized the electron arrangement and the larger the atoms' partial charges.
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Neptune has a mass that is about 17 times the mass of earth. the distance between the sun and neptune is about 30.1 times the distance between the sun and earth. if the gravitational force between the sun and earth is 3.5 x 1028 n, which is closest to the force between neptune and the sun? 6 x n 6 x n 6 x n 6 x n
We would weigh 114 kg on Neptune if we weighed 100 kg on Earth. In comparison, we would experience much lower gravity on the Moon (16.5%) or Mars (37.6%).
Neptune is much larger than Earth. In fact, its mass is 17 times that of the Earth. Neptune's surface gravity is approximately 110% that of Earth's, so if you weigh 100 pounds on Earth, you would weigh 110 pounds on Neptune (assuming you could find someplace to, well, stand). M is subdivided into two parts, m1 and m2. The ratio of m1/M for which the gravitational attraction between the two parts becomes maximum at a given separation is. 1:1.
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Answer:
6 x 10^26 N
Explanation:
testing of a light switch is being discussed. technician a says a switch can be tested with a voltmeter. technician b says to use a fused jumper wire to see if the switch is operating. who is correct?
Both technician are correct .
What is voltmeter ?
A voltmeter, also known as a voltmeter, is an instrument used to measure the potential difference or voltage between two points in an electrical or electronic circuit. Some voltmeters are intended for use on direct current (DC) circuits. Others are designed for AC circuits. A dedicated voltmeter can measure radio frequency (RF) voltage.
A simple analog voltmeter consists of a sensitive galvanometer (ammeter) in series with a high resistance. The internal resistance should be high inside . Otherwise, significant currents will flow and interfere with the operation of the circuit under test. The sensitivity of the galvanometer and the value of the series resistance determine the range of voltages the meter can display.
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Energy that comes from sources whose supplies are capable of being regenerated or are virtually inexhaustible is called.
Answer: Renewable
Explanation: Hope this helps.
On average, there is enough wind in the UK each year to supply all of the UK's electricity needs.
Explain why the UK may still need power stations that use fuel to generate electricity
Explanation:
Unplanned maintenance at nuclear plants and lower than average wind speeds mean the country is currently relying on gas-powered stations to generate about half its electricity.
during a snowball fight two balls with masses of 0.30 and 0.70 kg, respectively, are thrown in such a manner that they meet head-on and combine to form a single mass. the magnitude of initial velocity for each is 12.0 m/s. what is the speed of the 1.0-kg mass immediately after collision?
Velocity can be defined as the rate at which something moves in a specific direction.as the speed of a car driving north on a highway or the pace at which a rocket takes off.Because the velocity vector is scalar, its absolute value magnitude will always equal the motion's speed.
Solve the problem ?
The direction of a body or object's movement is defined by its velocity.In its basic form, speed is a scalar quantity.In essence, velocity is a vector quantity.It is the speed at which distance changes.It is the displacement change rate. Velocity is the pace and direction of an object's movement, whereas speed is the time rate at which an object is travelling along a path.In other words, velocity is a vector, whereas speed is a scalar value. 10.4 m/sGiven that the weight of the first snowball, m1, is 0.3 kg, and the weight of the second snowball, m2, is 0.7 kgu = I2.0 m/s is the magnitude of the starting velocity for both masses.The magnitude of starting momentum is equal to the magnitude of final momentum, according to the formula for the conservation of linear momentum.V(m1 + m2) = m1u1 + m2u2.
0.3 * 12.0 + 0.7 * 10.4 = V(3.0 + 7.28)
3.0+ 7.28 = V(1) (1)
10.28 = V
The 0.3 mass and 0.7 kg mass are added to create the 1 kg mass
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The 0.3 mass and 0.7 kg mass are added to create the 1 kg mass.
What is Velocity?The velocity of a body or object determines its direction of motion. Speed is a scalar quantity in its most fundamental form. Velocity is essentially a vector quantity. It is the rate of change in distance. The displacement change rate is the issue.Speed is the rate at which an object travels along a path over time, whereas velocity is the speed and direction of an item's motion.In other words, speed is a scalar value, but velocity is a vector.10.4 m/sGiven that the first snowball, m1, weighs 0.3 kg, and the second snowball, m2, weighs 0.7 kg, the beginning velocities of both masses are equal at u = I2.0 m/s.
V(m1 + m2) = m1u1 + m2u2.
0.3 * 12.0 + 0.7 * 10.4 = V(3.0 + 7.28)
3.0+ 7.28 = V(1) (1)
10.28 = V
The 0.3 mass and 0.7 kg mass are added to create the 1 kg mass.
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What is the focal length of a concave lens that forms an image with a xi value of -10.0 cm when an object is 35.0 cm from the lens?
Answer:
1 / f = 1 / object + 1 / image = 1 / 35 - 1 / 10 thin lens equation
f = o * i / (o + i)
f = -10 * 35 / (-10 + 35) = -350 / 25 = -14 cm
Reflect on the claims and the evidence you examined today. At this point, which claim do you think is best supported by the evidence?
Claim 1: There is frozen water in tank 2, which is blocking some of the oxygen from going into tank 3.
Claim 1: , There is frozen water in tank 2, which is blocking some of the oxygen from going into tank 3.
Claim 2: Some of the liquid oxygen evaporated in tank 3.
Claim 2:, Some of the liquid oxygen evaporated in tank 3.
Claim 3: Some of the oxygen didn’t condense in tank 2.
Claim 3:, Some of the oxygen didn’t condense in tank 2.
In the space below, explain your claim choice using the evidence you discussed today.
Claim 2: Some of the liquid oxygen evaporated in tank 3 is the claim with the most proof based on the experiment with liquid oxygen and nitrogen.
In the propellant systems of missiles and rockets, liquid oxygen is employed as an oxidant for liquid fuels. In addition to acetylene and other fuel gases, oxygen is frequently used in the metal industry for metal cutting, welding, scarfing, hardening, cleaning, and melting.Therefore, the reason of above statement can be explained as, that nitrogen has a lower boiling point than oxygen, the liquid nitrogen and oxygen mixture in tank 3 is slightly heated to allow nitrogen to escape. However, as gas particles can evaporate at a temperature below their boiling point provided they have enough energy, some oxygen might have escaped simultaneously when the boiling produced sufficient energy.
Thus the claim 2 is suitable option of this evidence.
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most interstellar clouds are made mostly of hydrogen (because hydrogen is the most common element in the universe). why are these clouds usually dominated by the color red?
The interstellar clouds that are made mostly of hydrogen are usually dominated by the color red because of its strong visible emission lines
Hydrogen is the most common element in the universe because a hydrogen is a pair of protons and electrons. Since they are oppositely charged they attract each other and it is easier to bond without the need of any external forces.
Red is colour in visible light spectrum with longest wavelength and has the lowest frequency. Because of its longer wavelength it can travel much farther distances than other colours in visible spectrum.
Therefore, these clouds usually dominated by the color red because of its strong visible emission lines
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Why do the planets orbit the Sun?
A. The sun has enough mass to attract the planets
B. The sun has enough heat to attract the planets
C. The sun has enough velocity to attract the planets
D. The sun has enough energy to attract the planets
A. The sun has enough mass to attract the planets. is the correct statement for the given question.
What are planets?A planet is a celestial body that revolves in an orbit around the Sun, planet has sufficient mass for self-gravity to overcome rigid body forces. It has space around its orbit to revolve around the sun. A gas Giant is a planet composed mainly of gas. Super-Earth is a rocky planet that is larger than Earth.
Neptune-like planets that are about the size of Neptune. A terrestrial is a rocky world that is outside our solar system. The basic reason the planets revolve around the Sun is the gravity of the Sun that keeps them in their orbits. As the Moon orbits the Earth because of the Earth's gravitational pull and the Earth orbits the Sun because of the Sun's gravitational pull.
So we can conclude that the planets orbit the Sun because the sun has enough mass to attract the planets.
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If air resistance can be neglected, what happens to the horizontal velocity
of a basketball as it is thrown to the basket from the free-throw line?
O decreases
O stays constant
O increases
increases while the ball is going up, and then decreases while the ball is coming
down
O decreases while the ball is going up, and then increases while the ball is coming
down
If air resistance can be neglected, what happens to the horizontal velocity of a basketball as it is thrown to the basket from the free-throw line increases while the ball is going up, and then decreases while the ball is coming down.
Does the horizontal velocity change if air resistance is neglected?- When anything is hurled horizontally, gravity accelerates the object downward. – The only direction in which gravitational acceleration occurs is vertical. If we exclude the effects of air resistance, the object's horizontal velocity remains constant.
We know that the horizontal component of the force acting on the projectile at any given time will be zero if the air resistance is ignored in the projectile motion, which results in Fx=0.
The only force operating on the body in a horizontal direction if we neglect air resistance is gravity, which is acting in a vertical direction. As a result, the horizontal motion moves at a constant speed.
Therefore, option C is correct.
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A car with a weight of 6996 N is subjected to a net force of 1.74e4. The cars acceleration will be
Answer: 24.37 m/s/s [forward] = a
Explanation:
First, find mass with the Fgrav formula.
Fgrav=mg
6996=m(9.8)
713.88 kg
Then, plug the answer into Newton's second law formula.
Fnet = ma
1.74e4 = (713.88)a
(1.74e4)/(713.88) = a
24.37 m/s^2 = a
A vector is 253 m long and points in a 55.8 degree direction. Find the y-component of the vector. Please help!!
Answer:
209.3 m
Explanation:
x component will be 253 cos 55.8
y component will be 253 sin 55.8 = 209.3 m
a comet is in an elliptical orbit around the sun. its closest approach to the sun is a distance of 4.5 multiply 1010 m (inside the orbit of mercury), at which point its speed is 8.9 multiply 104 m/s. its farthest distance from the sun is far beyond the orbit of pluto. what is its speed when it is 6 multiply 1012 m from the sun? (this is the approximate distance of pluto from the sun.) speed
An elliptical orbit of a comet around the sun. The Pluton orbit is far from the sun's farthest distance. 51109.88 m/s is the speed when it is 6 x 1012 m from the sun.
given data
Vi=9.2104m/s is the comet's speed at d1=4.51010m.
When d2=61012m, the speed will be Vf.
Since there is no work done by the environment and the system's starting and final energies are equal, we can use:
[tex]E_{f}=E_{i}+W\\K_{f}+U_{f}=K_{i}+U_{i}+0\\1/2mv_{f}^{2}+\frac{-GMm}{d_{2}}=1/2mv_{i}^{2}+\frac{-GMm}{d_{i}} \\v_{f}=\sqrt{v_{i}^2+2GMm[1/d_{2}-1/d_{1}]}[/tex]
Substitute the given values to find final velocity Vf
So
[tex]v_{f}=\sqrt{(9.2*10^{4}m/s )^2+2(6.7*10^{-11})(1.98*10^{30})[1/6*10^{12}-1/4.5*10^{10}]} \\[/tex]
[tex]v_{f}[/tex]=51109.88m/s
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