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. from Physics Motion in A Plane Class 11 Manipur Board
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Physics Part I

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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.

Given,

Range, 
R = 3 km

Angle of projection, θ = 30° 

Acceleration due to gravity, g = 9.8 m/s

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

       R = u02 Sin 2θ / 

i.e.,  3 = u02 Sin 600 / g 

         u02 / 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 = u02 / g                                 ...(ii)

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

Rmax = 3√

        = 2 X 1.732 = 3.46 km 

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