What is the speed of the bullet? Answer in units of m/s

Question

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance 72 cm apart on the same axle. From the angular displacement 32.1 ◦ of the two bullet holes in the disks and the rotational speed 862 rev/min of the disks, we can determine the speed of the bullet.

Answer 1

Hi Sam A.,

Nice problem. When the bullet is shot at the two rotating disks (862 rev/min), it penetrates the first disk at time t₁, then a distance of 72 cm, and a later time t₂, it passes through the second disk, with an angular displacement of 32.1⁰.

We can find the time t it takes the disk to rotate 32.1⁰ which is the same time t it takes the bullet to travel 72 cm = 0.72 m (since we need m/s in our answer).

First lets find the time it takes for the angular displacement of 32.1⁰:

t = (min/862 rev)*(1 rev/360 degrees)*(60 sec/1 min)* 32.1 degrees = 0.006206 sec

Then the speed of the bullet is:

|v| = 0.72 m/0.006206 s = 116 m/s

I hope this helps, Joe.

Answer 2

You need to find the time interval Δt between the bullet striking the 2 disks, and then divide the distance between the disks (0.72 m) by the time in seconds, to get speed in m/s. Here are the steps:

Convert the angular displacement of 32.1° to radians.

Δθ = 32.1(π/180) radians

Find angular speed in radians per second

ω = 862(2π)/60 radians per second

Δt = Δθ / ω (result will be in seconds)

Finally, divide the disk separation distance (0.72 m) by Δt in seconds, and get the bullet speed in m/s. You now have all you need to solve the problem. You finish from here.