Question

Two rifles are fired at targets, which are 100 m away. The first rifle fires bullets at 1200 ft/s and the second fires a bullet at 3000 ft/s. How long will it take each bullet to get to the target? If both are aimed directly at the bull's-eye, how far will each bullet travel below the bull's-eye?

Answer 1

let α be the angle of the projectile with the horizontal as it leaves the muzzle.
Here α=0 degree.
Let vi=initial muzzle velocity, then
horizontal velocity, vh=vi*cos(α).

Time taken to reach the target
t=Horizontal distance/vh
where horizontal distance = 100m

Since acceleration due to gravity acts on the bullet during this time, then
vertical displacement
Dv=vi*sin(α)t-(1/2)gt²
where Dv is negative downwards.

Use consistent units in the above equations, for example metres and seconds.