Question

An artillery piece which consistently shoots its shells with the same muzzle speed has a maximum range $R$ . To hit a target which is $\frac{R}{2}$ from the gun and on the same level, the angle of elevation of the gun should be

• A. $15^\circ $
• B. $45^\circ $
• C. $30^\circ $
• D. $60^\circ $

Answer 1

Answer: (A)

$R_{\text{max}}=R=\frac{u^{2}}{g}$ (at an angle of $45^\circ $ )
$u^{2}=Rg$
Using $\text{Range}=\frac{u^{2} \text{sin} 2 \theta }{g}$
then $\frac{R}{2}=\left(\textit{Rg}\right)\frac{\text{sin} 2 \theta }{g}$
$\text{sin} 2 \theta = \frac{1}{2}$
$2\theta =30^\circ \Rightarrow \theta =15^\circ $