Question

A projectile can have same range from two angles of projection with same initial speed. If h₁ and h₂ be the maximum heights, then

Moderate

Solution

$R = \frac{u^{2} \sin θ}{g} at angles θ and 90 ° - θ$
Now, $h_{1} = \frac{u^{2} \sin^{2} θ}{2 g} and h_{2} = \frac{u^{2} \sin^{2} (90 ° - θ)}{2 g} = \frac{u^{2} \cos^{2} θ}{2 g}$
$h_{1} h_{2} = {(\frac{u^{2} \sin 2 θ}{g})}^{2} \cdot \frac{1}{16} = \frac{R^{2}}{16}$
$∴ R = 4 \sqrt{h_{1} h_{2}}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

SCAN ME