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 66 cm apart on the same axle. From the angular displacement 23.9 ◦ of the two bullet holes in the disks and the rotational speed 1237 rev/min of the disks, we can determine the speed of the bullet.

Answer 1

For this problem we have a linear speed and an angular speed, but they do not convert to each other. What does connect them is the common element of time to reach one point to the other.

We will need to make all the units consistent.

The axle rotates at 1237 rev/m =1237(2π)/60s = 129.5 rad/s

The axle rotates 23.9° = 23.9(2π)/360° = 0.4171 rad

So the time elapsed is 0.4171/129.5 = 0.00322 s

The speed of the bullet can be determined using this time and the distance traveled so v = 0.66m/0.00322s = 205 m/s