Question

A juggler tosses a ball up in the air with initial speed $u$. At the instant it reaches its maximum height $H$, he tosses up a second ball with the same initial speed. The two balls will collide at a height

• A. $\frac{H}{4}$
• B. $\frac{H}{2}$
• C. $\frac{3H}{4}$
• D. $\sqrt{\frac{3}{4}}H$

Answer 1

The correct option is A $\frac{H}{4}$

Let they meet after t time. At the top u becomes 0

Distance traveled $d_1=\frac{g{t}^2}{2}$

Distance traveled by other is $d_2=ut-\frac{g{t}^2}{2}$

also $d_1+d_2=H$

on solving above equation we get $t=\frac{H}{u}$

also $H=\frac{u^2}{2g}$

on solving euation 2 we get $d_2=\frac{3H}{4}$