A child, hunting for her favorite horse, is running on the ground around the edge of a stationary merry-go-round. The angular speed of the girl has a...

A child, hunting for her favorite horse, is running on the ground around the edge of a stationary merry-go-round. The angular speed of the girl has a constant value of .250 rad/sec. 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 moving.) with a constant angular acceleration of 0.010 rad/s^(2). What is the shorest time it takes for the child to catch up with the horse?