Question

If a train is retarding and at same time a coin is thrown upwards, then you will observe that:
A) The coin reaches again in your hand
B) The coin falls behind you
C) The coin falls in front of you
D) The coin follows a circular path

Answer 1

When a vehicle travels, all the persons or things inside the vehicle will have the same velocity of the vehicle. Whenever a particular body which was in a moving vehicle loses its contact with the vehicle, the body will have a velocity of the vehicle at that particular time.

Complete step by step solution:
Let’s discuss the velocity of a vehicle and the velocity of the bodies in that vehicle. When a vehicle travels in a uniform or changing velocity, all the bodies inside the vehicle will also have the same velocity as the vehicle. And this changes only when the body and the vehicle get apart, that is when the body is not resting at the vehicle.

Here, we are discussing the velocity of a train and a thrown coin which was in the train. We know, the train is retarding and losing its speed by the time. When a coin is thrown upwards, the coin will have a velocity of the train at the exact time when the coin loses its contact with the hand and we take the time as zero.
That is, at $t = 0$ ,
Velocity of train= $v$
Velocity of coin= $v$ (In the direction velocity of the train)
We take the time as $t$ when the coin reaches back.
That is, at $t = t$
Velocity of train= $v - \Delta v$
Velocity of coin= $v$
(Where, $\Delta v$ is the change in velocity of the train due to the retardation.)
Distance covered by the coin= $t \times v$
Distance covered by the train= $t \times \left( {v - \Delta v} \right)$
From the given equations it is clear that the coin travels more distance than the train by the time $t = t$ . That is, the coin will fall in front of the hand.

The answer is option (C).

Note: Everything inside the vehicle is going at the vehicle's speed if the vehicle's speed .if the vehicle met with an accident, all the bodies inside the vehicle which are not made sure about inside the vehicle, including you not wearing a safety belt, would be brought to an end by parts of the vehicle before you.