Question

It was known that a shell fired with a given velocity and at an angle of projection $\frac{5\pi }{36}$ radian can strike a target but a hill was found to obstruct its path. The angle of projection to hit the target should be

• A. $\frac{23\pi }{36}$ radian
• B. $\frac{13\pi }{36}$ radian
• C. $\frac{10\pi }{36}$ radian
• D. Data is insufficient

Answer 1

The correct option is B $\frac{13\pi }{36}$ radian

We know $\tan \theta =\frac{4H}{R}$
$H=\frac{R\tan \theta }{4}$
H should be greater if the shell should hit the target without obstruction , for same Range . Hence , $\tan \theta$ should be higher .
We also know that there can be only $2$ angles of projection for a given range , $\theta$ and $\frac{\pi }{2}-\theta$ . Hence , $\frac{13\pi }{36}$ is the answer .