Question

The horizontal range of a projectile fired at an angle of $15^{o}$is 50 m. If it is fired with the same speed at an angle of $45^{o}$, its range will be

• A. 60 m
• B. 71 m
• C. 100 m
• D. 141 m

Answer 1

Answer: (C)

100 m

Answer 2

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

For the same speed , $R \propto \sin 2\theta$

$\therefore\frac{R_{1}}{R_{2}} = \frac{\sin 2 \times 15{^\circ}}{\sin 2 \times 45{^\circ}} = \frac{\sin 30{^\circ}}{\sin 90{^\circ}}$

Or $R_{2} = R_{1}\frac{\sin 90{^\circ}}{\sin 30{^\circ}} = 50m \times \frac{1}{\left( \frac{1}{2} \right)} = 100m$