Question

A train is standing on a platform. A man inside a compartment of the train drops a stone. At the same instant, the train starts to move with constant acceleration. The path of the particle as seen by the man who drops the stone is:

• A. parabola
• B. straight line for sometime & parabola for the remaining time
• C. always a straight line
• D. variable path that cannot be defined

Answer 1

The correct option is C always a straight line

From the ground FOR, for the stone,
$a_{sx}=0,a_{sy}=-g,u=0$
Since person inside train has acceleration same as that of the train $a_{tx}=+a$
Relative to the person in the train, acceleration of the stone is:
$a_{st}=0-a=-a,a_{yt}=-g$ and $u=0$
$a_{net}=-a\hat{i}-g\hat{j}$ \)
Velocity of stone at time $t$ after dropping, as seen from the train
$v=u+a_{net}t==(-a\hat{i}-g\hat{j})t$
Hence, stone will appear for the man inside the train, to move in a straight line path, along the direction of net acceleration.