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

Answer 1

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

Let $H_1$ and $H_2$ corresponds to the maximum height for projection angle $\theta$ and $(90-\theta )$ respectively.
So, we have
$\frac{H_1}{H_2}=\frac{u^2{\sin }^2\theta /2g}{u^2{\sin }^2({90}^{\circ }-\theta )/2g}={\tan }^2\theta$