Question

A bullet fired at an angle of ${15}^o$ with the horizontal hits the ground $6km$ away. Keeping the same velocity of projection for the bullet to attain a range of $12km$, the angle of projection should be:

• A. ${15}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. ${60}^o$

Answer 1

Answer: (C)

${45}^o$

Range in a projectile is given by:

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

$\frac{R_1}{R_2}=\frac{\sin 2{\theta }_1}{\sin 2{\theta }_2}=\frac{6}{12}=\frac{\sin {30}^o}{\sin 2{\theta }_2}$

$\Rightarrow \sin 2{\theta }_1=2\sin {30}^o=1$
$\Rightarrow 2{\theta }_2={90}^o$
$\Rightarrow {\theta }_2={45}^o$