Construct a sinusoidal function with the provided information, and then solve the equation for the requested values.

Question

A Ferris wheel is 20 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 4 minutes. How much of the ride, in minutes, is spent higher than 14 meters above the ground? (Round your answer to two decimal places.) 

Answer 1

The rate of angular motion is ω = 2pi rad/4 min = pi/2 rad/min

Using the math angle the y component will be y = 20sin(ωt - π/2) + 22

when the t = 0 the math angle will be -π/2 or 90º down from hub. In math coordinates the y based on the ngle is Rsin(θ). And we have to account for the circular motion being displaced upwards by R+2 meters.

Solve for the two values of sin that will yield y = 14 and calculate (θ₂ - θ₁)/ω to find time interval.