Question

It was calculated that a shell when fired from a gun with a certain velocity and at an angle of elevation $\frac{5\pi }{36}$ rad should strike a given target in the same horizontal plane. In actual practice, it was found that a hill just prevented the trajectory. At what angle of elevation should the gun be fired to hit the target.

• A. $\frac{5\pi }{36}rad$
• B. $\frac{11\pi }{36}rad$
• C. $\frac{7\pi }{36}rad$
• D. $\frac{13\pi }{36}rad$

Answer 1

The correct option is D $\frac{13\pi }{36}rad$

Same horizontal displacement is obtained in projectile motion for angles of projection of:
$\theta and\frac{\pi }{2}-\theta$
Hence the two pairs are.
$\frac{5\pi }{36}and\frac{13\pi }{36}$
Hence it will only hit the target if fired at $\frac{13\pi }{36}$
Hence option D is correct.