Question

The range $R$ of projectile is same when its maximum heights are $h_1$ and $h_2$. What is the relation between $R,h_1$ and $h_2$?

• A. $R=\sqrt{h_1{h}_2}$
• B. $R=\sqrt{2h_1{h}_2}$
• C. $R=2\sqrt{h_1{h}_2}$
• D. $R=4\sqrt{h_1{h}_2}$

Answer 1

The correct option is D $R=4\sqrt{h_1{h}_2}$

Range is same for angles of projection $\theta$ and $90-\theta$,
$R=\frac{u^2\sin \theta }{g},h_1=\frac{u^2{\sin }^2\theta }{2g}$
and $h_2=\frac{u^2{\sin }^2(90-\theta )}{2g}=\frac{u^2{\cos }^2\theta }{2g}$.
Hence $\sqrt{h_1{h}_2}=\frac{u^2\sin \theta \cos \theta }{2g}=\frac{1}{4}\left[\frac{u^2\sin 2\theta }{g}\right]=\frac{R}{4}$.