A bullet fired at an angle of 30° with the ...

Motion in a Plane

Question : 29 of 32

Marks: +1, -0

A bullet fired at an angle of 30° with the horizontal hits the ground 3.0 km away. By adjusting its angle of projection, can one hope to hit a target 5.0 km away? Assume the muzzle speed to be fixed, and neglect air resistance.

Solution:

Horizontal range,

R=\frac{u^{2} \sin 2\theta}{g}

3=\frac{u^{2} \sin 60^{\circ}}{g}=\frac{u^{2}}{g} \frac{\sqrt{3}}{2}

nce the muzzle velocity is fixed, therefore, Maximum horizontal range,

R_{\text{max}}=\frac{u^{2}}{g}=2\sqrt{3}=3.464\text{m}

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