Question

A large rectangular box $ABCD$ falls vertically with an acceleration $a$. A toy gun fixed at $A$ and aimed towards $C$ fires a particle $P$.

• A. $P$ will hit $C$ if $a=g$
• B. $P$ will hit the roof $BC$ if $a>g$
• C. $P$ will hit the wall $CD$ or the floor $AD$ if $a<g$.
• D. May be options either $\left(A\right),\left(B\right)$ or $\left(C\right)$, depending on the speed of projection of $P$.

Answer 1

Answer: (A), (B), (C)

The correct options are
A $P$ will hit $C$ if $a=g$
B $P$ will hit the roof $BC$ if $a>g$
C $P$ will hit the wall $CD$ or the floor $AD$ if $a<g$.

$a_{rel}=g-a$
If relative acceleration is zero then the fired particle will not get deviated from its path and it will hit the point C.
If $a>g$ then there is a relative acceleration in upward direction which will result in an unwanted velocity in upward direction. This results in the particle hitting the roof.
If $a<g$ then there is a relative acceleration in downward direction which will result in an unwanted velocity in downward direction. This results in the particle hitting the bottom or side CD.