Answer in m/s.

The speed of a moving bullet can be determined by allowing the bullet to pass through two rotating paper disks mounted a distance 88 cm apart on the same axle. From the angular displacement 18.4 degrees of the two bullet holes in the disks and the rotational speed 634 rev/min of the disks, we can determinethe speed of the bullet.

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

Ok so I know I have to convert 88cm to meters which comes out to 0.88m, the 18.4 degrees to radians which comes out to 0.3211406 radians. 634 rev/min comes out to 66.3587 rad/s. I am stuck after that. If anyone can please help it would be greatly appreciated! Thanks!

In the time it takes for the bullet to pass the 88 cm between discs, the first disc hit rotates 18.4 degrees relative to where the second disc is hit. The elapsed time is therefore

18.4 degrees/[634rev/min*360deg/rev*1min/60s)
= 18.4 degrees/3804 deg/s)= 0.00484 s
Divide 0.88 m by 0.00484 s for the bullet speed.

I get 182 m/s.. about half the speed of sound. That is rather slow for a bullet.

To determine the speed of the bullet, you can use the relationship between linear and angular speed. The linear speed v is given by v = rω, where r is the radius and ω is the angular speed.

Given:
- The distance between the two bullet holes in the disks (radius) is 0.88 m.
- The angular displacement of the bullet holes is 0.3211406 radians.
- The rotational speed of the disks is 66.3587 rad/s.

First, we can find the time it takes for the bullet to pass through the disks by using the formula t = θ/ω, where θ is the angular displacement and ω is the angular speed.

t = 0.3211406 rad / 66.3587 rad/s = 0.004840 s

Next, we can find the linear speed of the bullet using the formula v = d/t, where d is the distance traveled by the bullet (equal to the diameter of the disks, 2r).

d = 2 * 0.88 m = 1.76 m

v = 1.76 m / 0.004840 s = 363.64 m/s

Therefore, the speed of the bullet is approximately 363.64 m/s.