Question

When a ball is thrown up vertically with velocity $v_0,$ it reaches a maximum height of $h$. If one wishes to triple the maximum height, then the ball should be thrown with velocity.

• A. $\sqrt{3}{v}_0$
• B. $3v_0$
• C. $9v_0$
• D. $\frac{3}{2}{v}_0$

Answer 1

The correct option is A $\sqrt{3}{v}_0$

Using the $3^{rd}$ equation of motion,
$v^2-u^2=2as$
$\Rightarrow O-v_{\circ }^2=2ah$
$\Rightarrow v_{\circ }^2=2gh$
(Upward is taken as positive)
$\therefore h\propto v_{\circ }^2$
$\therefore$ to triple the maximum height, ball should be thrown with $\sqrt{3}{v}_{\circ }$