Question

Sachin (S) hits a ball along the ground with a speed $u$ in a direction which makes an angle ${30}^{\circ }$ with the line joining him and the fielder Prem (P). Prem runs to intercept the ball with a speed $\frac{2u}{3}.$ At what angle should he run to intercept the ball?

• A. ${\sin }^{-1}\left[\frac{\sqrt{3}}{2}\right]$
• B. ${\sin }^{-1}\left[\frac{2}{3}\right]$
• C. ${\sin }^{-1}\left[\frac{3}{4}\right]$
• D. ${\sin }^{-1}\left[\frac{\sqrt{4}}{5}\right]$

Answer 1

The correct option is C ${\sin }^{-1}\left[\frac{3}{4}\right]$

Ball moves with a velocity $u$ making an angle of ${30}^o$ with the line $SP$.

Let the fielder moves with velocity $\frac{2u}{3}$ in a line making an angle $\theta$ with $SP$.

Now for the fielder to intercept the ball, the velocity of ball as well as the fielder in a direction perpendicular to line $SP$ must be equal.

$\therefore$ $u$ $sin30=\frac{2u}{3}sin\theta$

$u\times \frac{1}{2}=\frac{2u}{3}sin\theta ⟹sin\theta =\frac{3}{4}$