Question

Two balls are projected at an angle $\theta$ and (90${}^{\circ }$ - $\theta$) to the horizontal with the same speed. The ratio of their maximum vertical heights is

• A. 1:1
• B. tan$\theta$ :1
• C. 1: tan$\theta$
• D. tan${}^2\theta$ : 1

Answer 1

The correct option is D tan${}^2\theta$ : 1

$H_1$ = $\frac{u^{2}si{n}^2\theta }{2g}$-----(i)

$H_2$ = $\frac{u^{2}si{n}^2(90-\theta )}{2g}$=$\frac{u^{2}cos2\theta }{2g}$----(ii)

Divide (i) by (ii), we get
$\frac{H_1}{H_2}$= $\frac{ta{n}^2\theta }{1}$