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

Answer 1

Answer: (C)

The ball will have same horizontal range if the angles of projection are $\theta$ and $\left(90^{\circ }-\theta \right)$.
$\therefore h_1=\frac{u^2{\sin }^2\theta }{2g}$ and
$h_2=\frac{u^2{\sin }^2\left(90^{\circ }-\theta \right)}{2g}$
$=\frac{u^2{\cos }^2\theta }{2g}$
$\therefore h_1+h_2=\frac{u^2}{2g}\left({\sin }^2\theta +{\cos }^2\theta \right)=\frac{u^2}{2g}$