Question

For angles of projection of a projectile at angles $({45}^{\circ }-q)$ and $({45}^{\circ }+q)$ the horizontal ranges described by the projectile are in the ratio of :-

• A. 1 :1
• B. 2 :3
• C. 1 :2
• D. 2 :1

Answer 1

The correct option is A 1 :1

$\frac{R_1}{R_2}=\frac{\frac{\left[u^2\sin 2\left(45-\theta \right)\right]}{g}}{\frac{\left[u^2\sin 2\left(45+\theta \right)\right]}{g}}$

$=\frac{u^2\sin \left(90-2\theta \right)}{u^2\sin \left(90+2\theta \right)}$

$=\frac{\cos 2\theta }{\cos \theta }=1$

Hence,

option $\left(A\right)$ is correct answer.