Q. From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards with the same speed (both vertically). If $v_A$ and $v_B$ are their respective velocities on reaching the ground then,
AMUAMU 2015Motion in a Plane
Solution:
Let the ball $A$ is thrown vertically upwards with speed $u$ and ball $B$ is thrown vertically downwards with the same speed $u$.
After reaching the highest point, $A$ comes back to its point of projection with the same speed $u$ in the downward direction. If $h$ be height of the building, then velocity of $A$ on reaching the ground is
$v^{2}_{A}=u^{2}+2gh$ or
$v_{A}=\sqrt{u^{2}+2gh}\,...\left(i\right)$
and that of $B$ on reaching the ground is
$v^{2}_{B}=u^{2}+2gh$ or
$v_{B}=\sqrt{u^{2}+2gh}\,...\left(ii\right)$
From eqns. $(i)$ and $(ii)$, we get $v_A = v_B$
