Question

The kinetic energy of a projectile at the highest point of it projection is $75$% of its kinetic energy at the point of projection. Find the angle of projection.

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${30}^{\circ }$
• D. ${53}^{\circ }$

Answer 1

The correct option is C ${30}^{\circ }$

Velocity at the highest point of an oblique projectile $=u\cos \theta$
According to question
$K{E}_{top}=\frac{75}{100}\times K{E}_{initial}$
$\Rightarrow \frac{1}{2}m{u}^2{\cos }^2\theta =\frac{3}{4}\times \frac{1}{2}m{u}^2$
$\Rightarrow \cos \theta =\frac{\sqrt{3}}{2}$
$\theta ={30}^{\circ }$