A merry-go-round is stationary. A dog is running on the ground just outside its

Question

A merry-go-round is stationary. A dog is running on the ground just outside its circumference, moving with a constant angular speed of 0.715 rad/s. The dog does not change his pace when he sees what he has been looking for: a bone resting on the merry-go-round one third of a revolution in front of him. At the instant the dog sees the bone (t = 0), the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.0155 rad/s^2. At what time will the dog reach the bone? ________ s. The confused dog keeps running and passes the bone. How long after the merry-go-round starts to turn do the dog and the bone draw even with each other for the second time? _________ s.

Explanation / Answer

In the below equations let d??, v=?, a=d?/dt

d = d? + v?t + at

For the merry-go -around
d =2pi/3+ at (d=0 is at the dog at t=0)

For the dog
d?=vt
d?=0.715t

You let d?=d and you get a quadratic

0=2pi/3 - 0.715t +at

If you solve this quadratic equation you get the answers...
t= 3.049 s
and
t= 91.620s

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