Question

Mary is riding a merry-go-round, whose radius is 25 feet and which is turning 36 degrees per second. Seeing a friend in the crowd, she steps off the the outer edge of the merry-go-round and suddenly finds it necessary to run? At how many miles per hour does she have to run?

Answer 1

since 1 revolution is 360 degrees,

(25 * 2π ft/rev) * (2π/10 rev/s) * 3600s/hr * 1mi/5280 ft = 10.71 mi/hr

Answer 2

At the moment she steps off, her linear velocity equals the rate the arc length is increasing.

circumference = 2π(25) = 50π ft
36° = 36/360 = 1/10 of a rotation

so the linear velocity of any point is 5π ft/second

5π ft/1 second
= (5π/5280) / (1/3600) miles/hour
= (5π/(5280)(3600) mph
= appr 10.7 mph