Question

A bullet fired at an angle of 30 degree with the horizontal hits the ground 3km away. By adjusting its angle of projection,can one hope to hit a target 5 km away? Assume the muzzle speed to be fixed and neglect air resistance. ( g=10m/s2). please show how to solve this question

Answer 1

yes one can adjust the angle and shoot at a distance of 5km.

Answer 2

Explanation:

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:

R = u02 Sin 2θ / g

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√3

= 2 X 1.732 = 3.46 km

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