Projection Under uniform Acceleration

Question

A ball is thrown from a point with a speed v_{0} at an angle of projection $\mathrm{\theta}.$ 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?

Easy

Solution

For the person to be able to catch the ball, the horizontal component of velocity of the ball should be same as the speed of the person, i.e.,

${\mathrm{v}}_{0}\mathrm{cos}\mathrm{\theta}=\frac{{\mathrm{v}}_{0}}{2}\text{of}\mathrm{cos}\mathrm{\theta}=\frac{1}{2}\phantom{\rule{1em}{0ex}}\text{of}\phantom{\rule{1em}{0ex}}\mathrm{\theta}={60}^{\circ}$

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