Question

A man on a rectilinear moving cart, facing the direction of motion, throws a ball straight up with respect to himslef. Then

• A. the ball will always return to him.
• B. The ball will never return to him.
• C. the ball will return to him if the cart moves with constant velocity.
• D. ball will return to him if cart has non-zero acceleration.

Answer 1

The correct option is C the ball will return to him if the cart moves with constant velocity.

Let velocity of cart w.r.t ground is $\overrightarrow{v_{C,G}}=u_x\hat{i}$
Let velocity of ball with respect to cart is,
$\overrightarrow{v_{B,C}}=u_y\hat{j}$
Hence, velocity of ball with respect to ground $\left(\overrightarrow{v_{B,G}}\right)$ is,
$\overrightarrow{v_{B,G}}=\overrightarrow{v_{B,C}}+\overrightarrow{v_{C,G}}$
$\Rightarrow \overrightarrow{v_{B,G}}=u_y\hat{j}+u_x\hat{i}$
$\overrightarrow{a_{B,G}}=-g\hat{j}=-10{\text{m/s}}^2\hat{j}$
$\because$ projected ball has velocity component in $x\&y$ directions w.r.t ground, and its acceleration is $g$ downwards.
$\Rightarrow$ path of ball will be parabolic and ball will have same $x-$ component of velocity as cart i.e $u_x$.
$\therefore$ Ball will always reach to man, Only if cart moves with a constant velocity.