Question

A projectile s aimed at a target on a horizontal plane but falls 8 m short, when the angle of projection is ${15}^0$, while it overshoots by 16 m, when the angle is ${35}^0$. The angle of projection to hit the target is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Let s be the distance of the target from the point of projection and u be the velocity of projection. Range of the projectile is given by the expression.
R = $\frac{u^{2}sin2\alpha }{g}\dots \dots \left(1\right)$

s - 8 = $\frac{u^{2}sin{(2\times 35)}^0}{g}\dots \dots \left(2\right)ands+16=\frac{u^{2}sin{(2\times 35)}^0}{g}\dots \dots \left(3\right)$

solving equations (2) and (3), we get s = 35.27 m and u = 23.35 m $s^{-1}$.
From equation (1), we get 35.27 = $\frac{\left(23.25\right)sin2\alpha }{g}\Rightarrow \alpha ={20.36}^0$