Question

A soldier is tasked with measuring the muzzle velocity of a new rifle. Knowing the principles of projectile motion, he decides to perform a simple experiment at the indoor firing range. The soldier hangs a target a distance of d = 103 m from the end of the barrel. The rifle is mounted so that the bullet exits moving horizontally at the same height as the bullseye. After several trials, the soldier finds that the bullet strikes the target an average of 7.5 cm, below the bullseye.

Answer 1

Let us consider the downwards as positive direction.

Gravitational acceleration = g = 9.81 m/s²

Initial velocity of the bullet = V₀

The bullet is moving horizontally initially.

Initial horizontal velocity of the bullet = V_x0 = V₀

Initial vertical velocity of the bullet = V_y0 = 0 m/s

Height the bullet strikes below the bullseyes = H = 7.5 cm = 0.075 m

Time taken by the bullet to reach the target = T

H = V_y0T + gT²/2

0.075 = (0)T + (9.81)T²/2

T = 0.12365 sec

Horizontal distance of the target = R = 103 m

There is no horizontal force on the bullet therefore the horizontal velocity of the bullet remains constant.

R = V_x0T

103 = V₀(0.12365)

V₀ = 833 m/s

Muzzle velocity of the rifle = 833 m/s