Question

A ball is thrown with a velocity of $40\text{m/s}$ at an angle of $60°$ with the horizontal from a point $A$ on the ground. A boy simultaneously starts from $A$ to move a constant velocity $v$ such that the ball is always overhead the boy. Then value of $v$ is

• A. $10\text{m/s}$
• B. $20\text{m/s}$
• C. $30\text{m/s}$
• D. $40\text{m/s}$

Answer 1

The correct option is B $20\text{m/s}$

Horizontal component of velocity of ball, $V_h=40\cos 60°=20\text{m/s}$
For ball to remain always overhead the boy, relative velocity of ball in horizontal direction w.r.t the boy i.e. $\left(V_{hb}\right)$should be zero.
${\overrightarrow{V}}_{\text{hb}}={\overrightarrow{V}}_{\text{h}}-{\overrightarrow{V}}_{\text{b}}$
$0=40\cos 60°-v\Rightarrow v=20\text{m/s}$