Question

A body is projected with a certain speed at angles of projection of $\theta$ and ${90}^o-\theta$ The maximum height attained in the two cases are $20m$ and $10m$ respectively. The maximum possible range is

• A. $60m$
• B. $30m$
• C. $20m$
• D. $80m$

Answer 1

The correct option is A $60m$

Maximum height in a projectile projected at an angle $\theta$ is given by:

$H=\frac{u^2{\sin }^2\theta }{2g}.....\left(1\right)$

$H_1=\frac{u^2{\sin }^2\theta }{2g}=20.....\left(2\right)$

$H_2=\frac{u^2{\sin }^2(90-\theta )}{2g}=\frac{v^2{\cos }^2\theta }{2g}=10......\left(3\right)$

$\frac{H_1}{H_2}={\tan }^2\theta =2......\left(4\right)$

$\Rightarrow \frac{u^2}{2g}=30$

Now, $R_{max}=\frac{u^2\sin 2\theta }{g}=60\sin 2\theta$$=60m(at\theta ={45}^o)$