Question

A child, hunting for his favorite wooden horse, is running on the ground around the edge of a stationary merry-go-round. The angular speed of the child has a constant value of 0.264 rad/s. At the instant the child spots the horse, one-quarter of a turn away, the merry-go-round begins to move (in the direction the child is running) with a constant angular acceleration of 0.00500 rad/s2. What is the shortest time it takes for the child to catch up with the horse?

Answer 1

The child reaches the horse when the angular positions of the child and horse, measured from initial angular position of the child, are the same.

0.264 t = (pi/2) + (1/2)(0.005)t^2

Solve for t in seconds.

The pi/2 term represents the quarter turn lead of the horse.