Question:
A bullet fired at an angle of 30 degree 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.
Answer:
Range, R = 3 km
Angle of projection, 
= 30°
Acceleration due to gravity, g = 
Horizontal range for the projection velocity
, is given by the relation:
The maximum range (
is achieved by the bullet when it is fired at an angle of 45°with the horizontal, that is,
On comparing equations (1) and (2), we get:
Hence, the bullet will not hit a target 5 km away.
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