A person flips a coin into the air and it lands on the ground a few feet away. S

Question

A person flips a coin into the air and it lands on the ground a few feet away. Suppose the person were to perform an identical coin flip on an elevator rising with constant upward acceleration. Would the coin's time of flight be greater than, less than, or equal to its time of flight when the person was at rest? greater than less than equal to Choose the best explanation from among the following: The elevator's upward speed increases during the coin's flight, and hence it catches up with the coin at a greater height than before. The coin's downward acceleration is less than before because the elevator's upward acceleration partially cancels it. The coin has the same acceleration once it is tossed, whether the elevator accelerates or not.

Explanation / Answer

I would like to discuss this problem in detail.

Case 1 : Coin flipped on ground

1) When we flip a coin in air while on ground, we impart a velocity to the coin by flipping it in air.

2) Assuming only grvitational force in existence, the coin keeps travelling up due to the imparted flipping velocity.But due to the retarding force of gravity (since it acts in downward direction) , the coin eventually reaches a height where its velocity in the upward direction becomes 0.

3) Since the gravitational force still exists, it starts acting on the vertical component of velocity and increases it in gravity's direction.( downward direction).

4) The vertical velocity keeps increasing till the coin hits the ground. This total time from flipping till hitting the ground is called time of flight.

NOTE: In this case, only the coin is trying to reach the ground as the ground isnt moving towards the coin.( I said this sentence because we know that the time of flight is recorded from flipping till it hits the ground/floor)

Case 2: Coin flipped in an elevator moving up with uniform velocity

NOTE: All observations are made with respect to ground.( not floor of the elevator)

1) When we flip a coin in an elevator with a uniform speed, the coin already has a speed due to the motion of the elevator. (with respect to earth!! as i have already mentioned).

2) So due to this extra velocity, the height attained by coin, before its vertical velocity becomes 0, is more that what it would have been in the case 1.

3) But, if we observe,the height is measured from the base where it is suppose to hit.In this case, the base is the floor of the elevator, which also has a velocity.

4) So, while the coin was busy attaining height, the elevator floor also elevated up due to its velocity.So, in reality the height gain will be exactly what it was in case 1 and hence the same time of flight.

5) In other words, if we observe the coin with respect to the elevator, it becomes the simple case 1 very neatly.

Case 3: Coin flipped in an elevator with constant upward acceleration

NOTE: All observations are made with respect to ground.( not floor of the elevator)

1) In this case, when we flip the coin, it will have the velocity of the elevator when flipped.(with respect to ground again!!).

2) Due to this extra velocity (apart from flipping velocity) , again the coin will reach more height than in case 1.

3) As we saw in case 2, the elevator will also try to cope up with the height which the coin has attained.

4) But here the velocity with which the elevator floor moves up is increasing due to the presence of accleration

5) Therefore on comparing the three cases simultaneously, we can qualitatively comment that the time of flight in the third case will be lesser than the above 2.

Important: When a body detaches from another body which is at velocity v and acceleration a, the detached body can only carry over the velocity from the parent body due to the property called inertia. Acceleration, cannot be carried like this.

In my opinion, the answer should be lesser time with the explanation which is given in case3 or Part B - option 1.

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