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

Question

A merry-go-round is stationary. A dog is running on the ground just outside the circumference, moving with a constant angular speed of 0.750 rad/s. The dog does not change his pace when he sees a bone resting on the edge of the merry-go-round one-third of a revolution in front of him. At the instant the dog sees the bone, the merry-go-round begins to move in the direction the dog is running, with a constant angular acceleration of 0.0150 rad/s2.

a. After what time will the dog reach the bone?

b. 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?

Explanation / Answer

= 0.750rad/s
= 0.0150rad/s².

for the dog
= t
for the merry-go-round
= (2/3) + ½t²
so the dog will reach the bone when
t = (2/3) + ½t²
gives the quadratic
½t² - t + (2/3) = 0

0.5*0.015*t^2 - (0.75*t) + (2*3.142/3) = 0

0.0075*t^2 - (0.75*t) + 2.094 = 0

by the quadratic formula
t 2.87 s & 97.12 s
are the answers to (a) & (b) respectively

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