temView?assignmentProblemID-83103293 previous 2 of 25 | ne Speed of a Bullet Par

Question

temView?assignmentProblemID-83103293 previous 2 of 25 | ne Speed of a Bullet Part A Derive a formula for the bullet speed u 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. distance D apart to a shaft turning with a rotational period T, as shown. Provide Feedbadk Continue Bullet Disk 1 Disk 2

Explanation / Answer

Given,

distance between the disks = D ;

rotation period = T ; angle between the position of the hole and that in second = theta

let t be the time taken to travel D(the distance between the beullets)

speed = dist/time=> distance = speed x time

D = vt => t = D/v (i)

for one rotation, if the disk rotates with period T,

theta = 2 pi t/T (ii)

putting the value of t from (i) to (ii) we get

theta = 2 pi D/vT

solving above equation for v, we get,

v = 2 pi D/ T theta

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