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Projectile Time, Height and Range

A bullet fire...

Question

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.

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Solution

Given: The angle of projection is 30° and the horizontal range for the given angle is 3 km.

The horizontal range of the projectile is given as,

R= u 2 sin2θ g …… (1)

By substituting the given values in the above expression, we get

3= u 2 sin2( 30° ) g u 2 g =3.464 km

For maximum range, put sin2θ=1 in equation (1).

The maximum range is given as,

R max = u 2 g =3.464 km

Thus, one cannot hit the target at 5 km away by adjusting the firing angle.

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