Question

The range of a projectile at an angle $\theta$ is equal to half of the maximum range if thrown at the same speed. The angle of projection is given by

• A. ${15}^{\circ }$
• B. ${30}^{\circ }$
• C. ${60}^{\circ }$
• D. Data insufficient

Answer 1

The correct option is A ${15}^{\circ }$

The range of the projectile is $R=\frac{u^2\sin 2\theta }{g}$
and $R_{max}=\frac{u^2}{g}$
here, $R=\frac{1}{2}\times R_{max}$
or $\frac{u^2\sin 2\theta }{g}=\frac{1}{2}\times \frac{u^2}{g}$
or $\sin 2\theta =1/2=\sin 30$
or $2\theta =30\Rightarrow \theta ={15}^o$