Question

A bullet leaving a rifle at an angle of 45 degrees travels a distance of 10 Km determine: A). The muzzle velocity B). What angle would you have to shoot the same bullet to go HALF the distance? Lower angle

Answer 1

First we need to derive the horizontal distance covered for a muzzle velocity of u, and angle with the horizontal θ.

The time t the bullet stays in the air is
Sy=0 = u*sin(θ)*t - (1/2)gt²
Solving for t gives t=2u*sin(θ)/g.

Substitute t in the usual formula for horizontal distance:
Sx=(u*cos(θ))*t
=2u²sin(θ)cos(θ)/g
=u²sin(2θ)/g ....(1)

For the present case,
Sx = 10,000m
Solve for in equation (1)
10000 = u²sin(2*45°)/g
u=sqrt(10000g/1)=313.05 m/s

To travel less distance horizontally, we cannot change u, but we can vary θ such that:
5000 = 313.05&aup2;*sin(2θ)/g
or
sin(2θ)=5000g/313.05²=0.5
asin(0.5)=30° or 120°.

Therefore θ can be 15° or 60°.