Question

From the ground, a projectile is fired at an angle of $60$ degrees to the horizontal with a speed of $20\, m/s^{-1}$. Take acceleration due to gravity as $10 \, m/s^{-2}$. The horizontal range of the projectile is

• A. $10 \sqrt{3}\, m $
• B. 20 m
• C. $20 \sqrt{3}\, m $
• D. $40 \sqrt{3}\, m $
• E. $400 \sqrt{3}\, m $

Answer 1

Answer: (C)

The horizontal range
$R=\frac{u^{2} \sin 2 \theta}{g}$
Given, $u=20 \,m / s$
$\theta=60^{\circ}$
$g=10 \,m / s ^{2}$
$R=\frac{(20)^{2} \sin \left(2 \times 60^{\circ}\right)}{10}$
$=\frac{20 \times 20}{10} \times \frac{\sqrt{3}}{2}=20 \sqrt{3} \,m$