Question

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

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

Answer 1

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

Initial velocity of the ball $=v_0$
Horizontal component of velocity of the ball $=v_0\cos \theta$
Person will be able to catch the ball if his velocity is the same as the horizontal component of velocity of the ball.
i.e$\frac{v_0}{2}=v_0\cos \theta \Rightarrow \cos \theta =\frac{1}{2}\Rightarrow \theta ={60}^{\circ }$

$\therefore$ Angle of projection of the ball must be ${60}^{\circ }$ if the person has to catch the ball.