Question

A gun is able to hit a target $100m$ away if it shoots at ${30}^o$. If the target moves $100m$ away from its original position, at what angle should the gun shoot?

• A. ${\sin }^{-1}\frac{1}{3}$
• B. ${\sin }^{-1}\frac{2}{3}$
• C. ${45}^o$
• D. Not possible to shoot the target

Answer 1

The correct option is D Not possible to shoot the target

Range of a projectile is given by
$R=\frac{u\sin \left(2\theta \right)}{g}$
Given,range is $100m$ when angle of projection is 30${}^o$,
therefore, $100=\frac{u}{g}\frac{\sqrt{3}}{2}$
$\frac{u}{g}=\frac{200}{\sqrt{3}}$
Now for range to be $200m$ $\sin \left(2\theta \right)$ should be equal to $\sqrt{3}$, which is not possible.