Question

A body is projected from the ground at an angle of ${\tan }^{-1}\left(\frac{8}{7}\right)$ with the horizontal. The ratio of the maximum height attained by it to its range is

• A. 8 : 7
• B. 4 : 7
• C. 2 : 7
• D. 1 : 7

Answer 1

Answer: (C)

For a projectile projected at angle $\theta$;
Maximum height, $H_{\max }=\frac{u^2{\sin }^2\theta }{2g}$
and range, $R=\frac{u^2\sin 2\theta }{g}$
$\therefore$ Ratio $=\frac{H_{\max }}{R}=\frac{\left(\frac{u^2{\sin }^2\theta }{2g}\right)}{\left(\frac{u^2\sin 2\theta }{g}\right)}=\frac{\tan \theta }{4}$
Here, $\theta ={\tan }^{-1}\frac{8}{7}$
$\Rightarrow \tan \theta =\frac{8}{7}=\frac{\frac{8}{7}}{4}=\frac{2}{7}$