How many seconds does it take a rider to travel from the bottom of the Ferris wheel to a point 30 feet above the ground?

Question

A Ferris wheel with a diameter of 50 feet makes one revolution every 40 seconds. How many seconds does it take a rider to travel from the bottom of the Ferris wheel to a point 30 feet above the ground? Note the formula for the length of an arc formed by a central angle with measure theta is s=2pi(r)(theta/360)

Answer 1

The angular velocity w = 2pi radians/40 seconds = pi/20 (radians/sec)

When the rider is 30 ft above the ground, he is 90 deg + tan-1(5/25) deg = 90 + 11.31 = 101.31 degrees = .5625pi radians along the ferris wheel circle.

Then, .5625pi radians/(pi/20)(radians/sec) = 11.257 seconds