Question

When a ball is thrown vertically upwards 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 $\sqrt{3}{v}_0$

By using third equation of motion
$v^2-v_0^2=2gh$
$\Rightarrow v_0^2=2g{H}_{\text{max}}$ (at $h=H_{\text{max}},v=0$)
$\Rightarrow H_{\text{max}}\propto v_0^2$
$\Rightarrow v_0\propto \sqrt{H_{\text{max}}}$
i.e., to triple the maximum height, ball should be thrown with velocity $\sqrt{3}{v}_0$.