Question

Two bodies are projected from the ground with the same speed. If the angles of their projection from the ground is ${45}^{o}and{15}^o$ 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 $2:1$

Let the speed of the projectiles be $u$.

First projectile $\theta ={45}^o$

Range $R_1=\frac{u^2\sin 2\theta }{g}=\frac{u^2\times \sin 90}{g}=\frac{u^2}{g}$

Second projectile $\theta ={15}^o$

Range $R_2=\frac{u^2\sin 2\theta }{g}=\frac{u^2\times \sin 30}{g}=\frac{u^2}{2g}$

So, $R_1:R_2=1:\frac{1}{2}=2:1$