A Ferris wheel with a radius of 13 m is rotating at a rate of one revolution every 2 minutes. How fast is a rider rising when the rider is 25 m above ground level?

Answer 1

Consider the axle to be at (0,13)
Then y=13+13sin(πt)
when y=25,
13sin(πt) = 12
sin πt = 12/13
Looks like the familiar 5-12-13 triangle, so cos(πt) = 5/13

dy/dt = 13πcos(πt) = 13π*5/13 = 5π m/min