Solve for minutes and seconds

Question

A Ferris wheel is 10 meters in diameter and boarded from a platform that is 1 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 2 minutes. How many minutes of the ride are spent higher than 7 meters above the ground? Give your answer correct to the nearest second.

_____minutes and _____ seconds

Answer 1

To be 7 meters above the ground, you need to be 6 meters above the platform or 1 meter above the center

line of the circle. This is at a point on a circle where sinθ = 1/5 or sin^-1(0.2) = θ ≈ 0.2 = 0.064π radians.

The change in angle to be above 7 meters, Δφ = π-2θ = 0.872π

The rotational velocity, ω= 2π/2 = π radians/minute.

time, t= Δφ/ω = (π-2θ)/π = .872 minutes ≈ 52 seconds