Question

A gun fires a bullet at a speed of $140m{s}^{-1}$. If the bullet is to hit a target at the same level as the gun and at $1km$ distance, the angle of projection may be:-

• A. ${60}^{\circ }$ or ${30}^{\circ }$
• B. ${40}^{\circ }$ or ${50}^{\circ }$
• C. ${15}^{\circ }$ or ${75}^{\circ }$
• D. ${20}^{\circ }$ or ${70}^{\circ }$

Answer 1

The correct option is C ${15}^{\circ }$ or ${75}^{\circ }$

Given that range, $R=1km=1000motor$

$u=140m/s$

but $R=\frac{u^2\sin 2\theta }{g}$

putting $g=9.8m/s^2$

we get $\sin 2\theta =\frac{Rg}{u^2}=\frac{1000\times 9.8}{140\times 140}$

$\sin 2\theta =0.5\Rightarrow 2\theta ={30}^o$

$\Rightarrow \theta ={15}^o$ or $90-15={75}^o$