Question

A body is projected with velocity $u$ at an angle $\theta$ with the horizontal. Another body having double mass is also projected with the same velocity but at an angle $90-\theta$. The ratio of their maximum heights is

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

Answer 1

The correct option is C

${\tan }^2\theta$

According to the question, $H_1=\frac{u^{2}si{n}^2\theta }{2g}$
and $H_2=\frac{u^{2}si{n}^2(90-\theta )}{2g}=\frac{u^{2}co{s}^2\theta }{2g}$
$\therefore \frac{H_1}{H_2}=\frac{si{n}^2\theta }{co{s}^2\theta }=ta{n}^2\theta$
Hence, the correct choice is (c).