Question

A ball is thrown from a point with a speed $v_0$ at an elevation angle of $\theta$. From the same point and at the same instant, a person starts running with a constant speed $\frac{v_0}{2}$ to catch the ball. Will the person be able to catch the ball? If yes, what should be the angle of projection?

• A. No
• B. Yes, ${30}^{\circ }$
• C. Yes, ${60}^{\circ }$
• D. Yes, ${45}^{\circ }$

Answer 1

The correct option is C Yes, ${60}^{\circ }$

Initial velocity of the ball = $v_0$
Horizontal component of velocity of the ball = $v_0\cos \theta$
He will be able to catch the ball if his velocity is the same as the horizontal component of velocity with which the ball is thrown.
$\Rightarrow \frac{v_0}{2}=v_0\cos \theta$
$\Rightarrow \cos \theta =\frac{1}{2}$
$\Rightarrow \theta ={60}^{\circ }$
$\therefore$ Angle of projection of the ball must be ${60}^o$ if the person has to catch the ball.