Question

A passenger in a moving train tosses a coin. If the coin falls behind him, the train must be moving with
A. An acceleration
B. A deceleration
C. A uniform speed
D. Any of the above

Answer 1

Hint: Try to picturise the scenario and use logic. If not, then, work out the two components of velocity of the coin. Check what happens to the train velocity and the component of coin velocity parallel to it.

Complete step by step answer:
Imagine you are the passenger who tossed the coin and it fell behind you. What happened? When you tossed the coin the horizontal velocity of the coin was equal to the train velocity. We know that in a projectile motion involving both x and y component of velocity the x component of velocity remains the same at the beginning and end of the journey.
So if the train velocity remains the same then the coin velocity in x direction and train velocity will be equal and it will return to your hand. But it fell behind you which means train velocity changed in that course of time.
Now let the x component of velocity be u which is equal to train velocity at the start of journey. For coin u remains constant. Let the time taken for the trajectory be t. So in time t let the coin traversed distance x.
Since it fell behind you means that you travelled a greater distance x+dx. In time t you were supposed to travel x but you travelled x+dx which directly implies that your velocity increased (train’s velocity). Therefore the train accelerated hence increasing the velocity as a = dv/dt.

So, the correct answer is “Option A”.

Note:
For uniform speed the coin will return to the passenger’s hand. In the case of deceleration the distance travelled by the passenger will be x-dx implying the velocity decreased in time t. Therefore the coin travelled x and the passenger x-dx i.e. the coin will fall in front of the passenger.