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.​

Answer 1

Answer

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.

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Answer 2

Answer:

Refer to the Attachment.

Hope it Helps !!!!