The speed of a moving bullet can be deter- mined by allowing the bullet to pass through
two rotating paper disks mounted a distance
61 cm apart on the same axle. From the
angular displacement 14° of the two bullet
holes in the disks and the rotational speed
1436 rev/min of the disks, we can determine
the speed of the bullet.

v = 381 m/s

Explanation:

Linear Speed

The linear speed of the bullet is calculated by the formula:

Where:

x = Distance traveled

t = Time needed to travel x

We are given the distance the bullet travels x=61 cm = 0.61 m. We need to determine the time the bullet took to make the holes between the two disks.

The formula for the angular speed of a rotating object is:

Where θ is the angular displacement and t is the time. Solving for t:

The angular displacement is θ=14°. Converting to radians:

The angular speed is w=1436 rev/min. Converting to rad/s:

Thus the time is:

t = 0.0016 s

Thus the speed of the bullet is:

v = 381 m/s