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 elevation angle of the gun should be:

Moderate

Solution

$R_{max .} = R = \frac{u^{2}}{g} or u^{2} = Rg Now, as range = \frac{u^{2} \sin 2 θ}{g} Then \frac{R}{2} = \frac{Rgsin 2 θ}{g} or \sin 2 θ = \frac{1}{2} = \sin 30^{\circ} θ = 15^{\circ}$

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