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Motion Under Variable Acceleration

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 the fixed, and neglect air resistance.

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Solution

Answer: No

Range, R = 3 km

Angle of projection, θ = 30°

Acceleration due to gravity, g = 9.8 m/s²

Horizontal range for the projection velocity u₀, is given by the relation:

The maximum range (R_max) is achieved by the bullet when it is fired at an angle of 45° with the horizontal, that is,

On comparing equations (i) and (ii), we get:

Hence, the bullet will not hit a target 5 km away.

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