Question

A railway compartment is $16m$ long, $2.4m$ wide and $3.2m$ 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 $g=10m/s^2$. Which of the following values of $u$ and $v$ is(are) correct?

• A. $v=20m/s$
• B. $u=3m/s$
• C. $v=15m/s$
• D. $u=2m/s$

Answer 1

Answer: (A), (B)

$u=3m/s$
$v=20m/s$

Consider the vertical motion of the particle after entering the compartment . Let it reach the floor in time $t$ .
$3.2=\frac{1}{2}\left(10\right)t^2\to t=0.8sec$
Due to the velocity component $u$ it covers $2.4m$ in this time .
Hence , $u=\frac{2.4}{0.8}=3m/s$
Also , the distance moved by the train in this time is the length of the train with speed $v$
Hence , $v=\frac{16}{0.8}=20m/s$