Question

From a building two balls $A$ and $B$ are thrown such that $A$ is thrown upwards and $B$ downwards (both vertically). If $v_{A}$ and $v_{B}$ are their respective velocities on reaching the ground, then :

• A. $v_{B}>y_{A}$
• B. $v_{A}=v_{B}$
• C. $v_{A}>v_{B}$
• D. their velocities depend on their masses

Answer 1

Answer: (B)

$v_{A}=v_{B}$

Answer 2

From conservation of energy, potential energy at height $h$ $= KE$ at ground Therefore, at height $h,$ PE of ball $A$ $PE =m_{A} g h$ $KE$ at ground $=\frac{1}{2} m_{A} v_{A}^{2}$ So, $m_{A} g h =\frac{1}{2} m_{A} v_{A}^{2}$ $v_{A} =\sqrt{2 g h}$ Similarly, $v_{B} =\sqrt{2 g h}$ Therefore, $v_{A}=v_{B}$ : In question it is not mentioned that magnitude of thrown velocity of both balls are same which is assumed in solution.