Question

When a ball is thrown vertically upwards with velocity $v_0$, it reaches a maximum height of $h$. With what velocity should the ball be thrown to reach half the maximum height.

• A. $\sqrt{2}{v}_0$
• B. $\sqrt{0.5}{v}_0$
• C. $\sqrt{1.5}{v}_0$
• D. $\sqrt{3}{v}_0$

Answer 1

The correct option is B $\sqrt{0.5}{v}_0$

By using third equation of motion
$v^2-u^2=2as$
$\Rightarrow v^2-v_0^2=2gh$
$\Rightarrow v_0^2=2g{H}_{\text{max}}$ (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 half the maximum height, ball should be thrown with velocity $\sqrt{0.5}{v}_0$.