Question

A shot is fired at an angle to the horizontal such that it strikes the hill while moving horizontally. Find initial angle of projection.

• A.
• B.
• C.
• D. none of these

Answer 1

The correct option is C

Method 1

Resolve along horizontal and vertical

Let the speed of projection by u

The projectile hits the plane at its maximum height as its moving horizontally. Also it would have moved a horizontal distance of $\frac{R}{2}$.

$H=\frac{u^{2}si{n}^2\theta }{2g};\frac{R}{2}=\frac{u^{2}sin\theta cos\theta }{g}$

Using trigo in the triangle we get

$tan{37}^{\circ }=\frac{H}{\left(R/2\right)}=\frac{\frac{u^{2}si{n}^2\theta }{2g}}{\frac{u^{3}sin\theta cos\theta }{g}}=\frac{3}{4}$

$\Rightarrow \frac{tan\theta }{2}=\frac{3}{4}$

$\Rightarrow tan\theta =\frac{3}{2}$