Chapter 7.3, Problem 106AE

The Ferris Wheel In 1893, George Ferris engineered the Ferris wheel. It was 250 feet in diameter. If a Ferris wheel makes 1 revolution every 40 seconds, then the function

$h\left(t\right)=125\sin \left(0.157t-\frac{\pi }{2}\right)+125$

represents the height $h$, in feet, of a seat on the wheel as a function of time $t$, where $t$ is measured in seconds. The ride begins when $t=0$.

a. During the first 40 seconds of the ride, at what time $t$ is an individual on the Ferris wheel exactly 125 feet above the ground?

b. During the first 80 seconds of the ride, at what time $t$ is an individual on the Ferris wheel exactly 250 feet above the ground?

c. During the first 40 seconds of the ride, over what interval of time $t$ is an individual on the Ferris wheel more than 125 feet above the ground?