Physics - Kinematics Question with Solution | TestHub

The range of a projectile is $R=\frac{u^2\sin (2\theta )}{g}$. Maximum range $R_{max}$ occurs at $\theta =45^{\circ }$, so $R_{max}=\frac{u^2}{g}$. We need to hit a target at $R_{max}/2$.

So, $\frac{R_{max}}{2}=\frac{u^2\sin (2\theta )}{g}$.

$\frac{1}{2}\frac{u^2}{g}=\frac{u^2\sin (2\theta )}{g}$.

$\sin (2\theta )=\frac{1}{2}$.

$2\theta =30^{\circ }$ or $2\theta =150^{\circ }$.

$\theta =15^{\circ }$ or $\theta =75^{\circ }$.

Both angles give the same range. Since $15^{\circ }$ is not an option, the answer is $75^{\circ }$.

The final answer is $\boxed{75^{\circ }}$.