Question

A ball is thrown from a point with a speed ${{\text{v}}_{\text{0}}}$ at an angle of projection $\theta .$ 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. Yes, ${{60}^{o}}$
• B. Yes, ${{30}^{o}}$
• C. No
• D. Yes, ${{45}^{o}}$

Answer 1

Answer: (A)

Yes, ${{60}^{o}}$

Answer 2

Man will catch the ball if the horizontal component of velocity becomes equal to the constant speed of man i.e, ${{v}_{0}}\cos \theta =\frac{{{v}_{0}}}{2}$ $\Rightarrow$ $\cos \theta =\frac{1}{2}$ $\Rightarrow$ $\cos \theta =\cos {{60}^{o}}$ $\therefore$ $\theta ={{60}^{o}}$