Question

The speed of a projected at its maximum height is half of its initial speed. The angle of projection is

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

Answer 1

The correct option is D ${45}^{\circ }$

A particle is projected with speed $um/s$ which is inclined at an angle $\theta$ with horizontal.

initial velocity of particle, $\overrightarrow{u}=u\cos \theta \hat{i}+u\sin \theta \hat{j}$

we know, at maximum height, only horizontal component of velocity exists.

so, velocity of particle at maximum height,

$\overrightarrow{v}=u\cos \theta \hat{i}$

a/c to question,

speed of project at its initial speed.

so, $2|\overrightarrow{v}|=|\overrightarrow{u}|$

$2u\cos \theta =u$

$\cos \theta =\frac{1}{2}$

$\theta =\frac{\pi }{3}$

hence, angle of projection is $\pi /3$