Question

What is the value of angle of projection for which the height of the projectile (H) and the range (R)of the projectile are the same?

Solution: Height and range

Maximum height of the projectile (H)

Height of the projectile (H)

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

Range of the projectile

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

$${H=R}$$

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

$${\frac{\sin^2\theta}{2}=2\sin\theta\cos\theta}$$

$${\frac{\sin\theta}{\cos\theta}=4}$$

$${\tan\theta=4}$$

$${\theta=\tan^{-1} (4)}$$

$${\theta=76^\circ}$$

Range of the projectile

Projectile motion: