Question

A boy throws a ball with a velocity $u$ at an angle $\theta$ with the horizontal. At the same instant, he starts running with uniform velocity to catch the ball before it hits the ground. To achieve this, he should run with a velocity of
(correct answer + 1, wrong answer - 0.25)

• A. $u\cos \theta$
• B. $u\sin \theta$
• C. $u\tan \theta$
• D. $\sqrt{u^2\tan \theta }$

Answer 1

The correct option is A $u\cos \theta$

Average velocity of boy should be $\frac{\text{range}}{\text{time of flight}}$
$\frac{\text{range}}{\text{time}}=\frac{\frac{u^2\sin 2\theta }{g}}{\frac{2u\sin \theta }{g}}=\frac{2u^2\sin \theta \cos \theta }{2u\sin \theta }=u\cos \theta$
Horizontal velocity should be same to catch the ball.