Question

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance 85 cm apart on the same axle. From the angular displacement 49 ◦ of the two bullet holes in the disks and the rotational speed 1142 rev/min of the disks, we can determine the speed of the bullet. 49◦ v 1142 rev/min 85 cm What is the speed of the bullet? Answer in units of m/s.

Answer 1

The bullet passes through the first disk and some time later passes through the second disk. The time it takes for the bullet travel the distance between the two disks is equal to the time it takes for the disks to rotate 49°. If we solve for this amount of time, we can then get the bullet's speed.

Calculate the amount of time it takes for the disks to rotate 49°. Apply this equation to the disks' rotational motion:

ω = θ/t

ω = angular velocity, θ = angular displacement, t = elapsed time

Given values:

ω = 1142rev/min = 6852°/s, θ = 49°

Plug in and solve for t:

6852 = 49/t

t = 7.151×10⁻³s

Calculate the bullet's speed. Apply this equation to the bullet's motion:

v = x/t

v = speed, x = distance between disks, t = elapsed time

Given values:

x = 85×10⁻²m, t = 7.151×10⁻³s

Plug in and solve for v:

v =  85×10⁻²/(7.151×10⁻³)

v = 120m/s