Tossing a Coin in a Moving Train

Try this beautiful problem, useful for Physics Olympiad, based on Tossing a Coin in a Moving Train.

The Problem: Tossing a Coin in a Moving Train

A person is sitting in a moving train and is facing the engine. He tosses up a coin that falls behind him. He concludes that the train is moving. A person is sitting in a moving train and is facing the engine. He tosses up a coin that falls behind him. He concludes that the train is moving-

(a) forward with increasing speed

(b) forward with decreasing speed

(c) backward with increasing speed

(d) backward with decreasing speed

Discussion: 

When the person throws up a coin in a train moving with uniform speed, the coin goes up with the initial velocity of the train. Hence, due to the inertia of motion, the coin will travel the same distance as the train and will fall in the hands of the person.

Now, if the train is accelerating i.e. the velocity of the train is increasing in the forward direction, the coin will fall behind the person as the distance covered by the train will be greater than that of the coin.

Also, if the train is going backward with decreasing speed, the distance covered by the coin will be greater than the distance covered by the train as the velocity of the train is gradually decreasing. Hence for this case also, the coin will fall behind the person.

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