Question

Two bodies are projected from the ground with the same speed. If the angles of their projection from the ground are ${45}^{\circ }$ and ${15}^{\circ }$ respectively, the ratio of their range is

• A. $1:2$
• B. $2:1$
• C. $\sqrt{3}:2$
• D. $1:\sqrt{2}$

Answer 1

The correct option is B $2:1$

Range of a body projected at an angle is R $=\frac{u^{2}sin2\theta }{g}$

Since the 2 bodies are projected with same initial velocities ,

$\frac{R_1}{R_2}=\frac{\sin 2x_1}{\sin 2x_2}$

$\frac{R_1}{R_2}=\frac{\sin 90}{\sin 30}$

Therefore the ratio, $\frac{R_1}{R_2}=2:1$