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.

 Range R of the projectile R = 3km

Angle of projection, =30o

Acceleration due to gravity, g = 9.8m/s2

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

R = uo2Sin2θ/g

3 = uo2Sin600/g

uo2/ g = 2√3 …….(i)

The maximum range (Rmax) is achieved by the bullet when it is fired at an angle of 45 with the horizontal, that is, Rmax = uo2/ g ….(ii)

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

Rmax = 2 × 1.732 = 3.46 km

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

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