Question

The range of a projectile fired at an angle of 15° is 50 m. If it is fired with the same speed at an angle of 45°,its range will be

Moderate

Solution

$\begin{aligned} R_{1} = \frac{u^{2} \sin 2 θ_{1}}{g}; R_{2} = \frac{u^{2} \sin 2 θ_{2}}{g} \\ \frac{R_{2}}{R_{1}} = \frac{\sin 2 θ_{2}}{\sin 2 θ_{1}} = \frac{\sin (2 \times 45^{\circ})}{\sin (2 \times 15^{\circ})} \end{aligned}$
$\begin{array}{l} = \frac{\sin 90^{\circ}}{\sin 30^{\circ}} = \frac{1}{1 / 2} = 2 \\ R_{2} = 2 R_{1} = 2 \times 50 = 100 m . \end{array}$

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