A bullet is shot through two cardboard disks attached a distance D apart to a sh

Question

A bullet is shot through two cardboard disks attached a distance D apart to a shaft turning with a rotational period T, as shown.

Derive a formula for the bullet speed v in terms of D, T, and a measured angle ? between the position of the hole in the first disk and that of the hole in the second. If required, use ?, not its numeric equivalent. Both of the holes lie at the same radial distance from the shaft. ? measures the angular displacement between the two holes; for instance, ?=0 means that the holes are in a line and ?=? means that when one hole is up, the other is down. Assume that the bullet must travel through the set of disks within a single revolution.

Explanation / Answer

here ,

Now , angle rotated = theta

time period = T

angular velocity , w = 2pi/T

Now , time taken for bullet to travel = time taken for the disk to rotate

theta/(2pi/T) = D/v

v = D *2pi/(T* theta)

the velocity of the bullet is D *2pi/(T* theta)

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