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Question

A railway compartment is 16 m long, 2.4 m wide and 3.2 m high. It is moving with a velocity v. A particle moving horizontally with a speed u, perpendicular to the direction of v, enters through a hole at an upper corner A and strikes the diagonally opposite corner B. Assume g=10m/s2. Which of the following values of u and v is(are) correct?

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A
v=20 m/s
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B
u=3 m/s
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C
v=15 m/s
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D
u=2 m/s
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Solution

The correct options are
B u=3 m/s
C v=20 m/s
Consider the vertical motion of the particle after entering the compartment . Let it reach the floor in time t .
3.2=12(10)t2t=0.8sec
Due to the velocity component u it covers 2.4m in this time .
Hence , u=2.40.8=3m/s
Also , the distance moved by the train in this time is the length of the train with speed v
Hence , v=160.8=20m/s

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