Question

A passenger in a moving train tosses a coin. If the coin falls behind him, the train must be moving:
(A) With a uniform speed
(B) With a deceleration
(C) With an acceleration
(D) Any of the above

Answer 1

Hint : Here we will use Newton’s laws of motion. Newton’s first law of motion, which is the law of inertia, states that any object will continue in its state of rest or uniform motion unless acted upon by some external force.

Complete step by step answer
The initial velocity of the coin just before the toss is the same as the velocity of the person on the train who tosses the coin whose velocity is equal to that of the train.
We need to assume here that the person tossing the coin is facing the same direction as the direction of motion of the moving train. This is the general assumption in such problems.
Once the toss has occurred, the coin loses contact with any object except air friction which is often neglected. Now when we impart a force on the coin for the toss we give it an upward force so that it moves up and drops down due to gravity. In the moving train, it will have the added velocity of the train itself which will remain after the toss since there is no external force acting on the coin opposing this horizontal motion.
On the vertical axis, gravity is acting downwards. Due to this external force, the initial velocity of the toss will be reversed once the coin drops down.
Therefore if the train moves at a uniform speed the coin should move along with the train in the horizontal direction.
However, in the problem, the coin falls behind the person. This would mean that the person went faster in the forward direction for the coin to drop behind him. Therefore the person must have accelerated since if he would have been moving with uniform velocity, he would have caught the coin. Since the person is on the moving train, the train must also be accelerating to assist the person in his acceleration forward.
Therefore the correct option is (C) With an acceleration.

Note
If the train is moving on a slope then the problem can become complicated depending on whether the slope is positive or negative. In this case, the horizontal velocity of the coin is also affected by gravitation. Considering only the above problem, another possible answer could be the train moving at a constant velocity in a positive slope so that the horizontal component of gravity pulls the coin backward.