Question

The horizontal range of projectile fired at ${75}^{\circ }$ is $R$. If it is fired with same speed at ${45}^{\circ }$, what would be its range?

• A. $\frac{R}{2}$
• B. $\frac{2R}{3}$
• C. $2R$
• D. $\frac{R}{3}$

Answer 1

The correct option is C $2R$

The general formula for Range is$\left(R=\frac{u^2\sin \left(2\theta \right)}{g}\right]$
Here, $R=\frac{u^2\sin \left(2\times {75}^o\right)}{g}$

For $\theta ={45}^o{R}^{\prime }=\frac{u^2\sin \left(2\times {45}^o\right)}{g}$
$\Rightarrow R^{\prime }=R/\sin \left({150}^o\right)$
hence $R^{\prime }=2R\left(\sin {150}^o=\frac{1}{2}\right)$