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)

$15^\circ$

Answer 2

$\text{R}_{\text{max}} = \text{R} = \frac{\text{u}^{2}}{\text{g}}$ (at an angle of $45^\circ$ $\text{u}^{2} = \text{Rg}$ Using $\text{Range} = \frac{\text{u}^{2} \text{sin} 2 \theta }{\text{g}}$ then $\frac{\text{R}}{2} = \left(\text{Rg}\right) \frac{\text{sin} 2 \theta }{\text{g}}$ $\text{sin} 2 \theta = \frac{1}{2}$ $2 \theta = 3 0^{\text{o}} \, \, \, ? \, \, \, \theta = 1 5^{\text{o}}$