Question

A ball is thrown from a point at different angles with same speed $u$ and has same range in both cases. If $h_{1}$ and $h_{2}$ are the heights attained in the two cases, then $\left(h_{1}+h_{2}\right)$ will be

• A. $\frac{u^{2}}{g}$
• B. $\frac{2 u^{2}}{g}$
• C. $\frac{u^{2}}{2 g}$
• D. $\frac{u^{2}}{4 g}$

Answer 1

Answer: (C)

The ball will have same horizontal range if the angles of projection are $\theta$ and $\left(90^{\circ}-\theta\right)$.
$\therefore h_{1}=\frac{u^{2} \sin ^{2} \theta}{2 g}$ and
$h_{2}=\frac{u^{2} \sin ^{2}\left(90^{\circ}-\theta\right)}{2 g}$
$=\frac{u^{2} \cos ^{2} \theta}{2 g}$
$\therefore h_{1}+h_{2}=\frac{u^{2}}{2 g}\left(\sin ^{2} \theta+\cos ^{2} \theta\right)=\frac{u^{2}}{2 g}$