A Ferris wheel has a radius of 20 m. Passengers get on halfway up on the right side. The direction of rotation is counter clockwise. The bottom of the Ferris wheel is 2 m off the ground. It rotates every 36 seconds.
a) Graph your height above the ground as a function of time
b) Determine a sine function that expresses your height as h as function of elapsed time t h(t)=20sin(πt/18)+22
c) Determine your height above the ground after 15 seconds algebraically.
After 15 seconds: h=20sin(15π/18)+22 =20sin(5π/6)+22 =20*(1/2)+22 =32 m
d) Determine the first time (to the nearest tenth) when your height is 38 m above the ground algebraically.
When h=38 m 38=20sin(πt/18)+22 38-22=20sin(πt/18) 20sin(πt/18)=16 sin(πt/18)=16/20=4/5=.8 arcsin(.8)=0.927 πt/18=0.927 (radians) t=(.927*18)/π≈5.31
Height above the ground after 15 seconds≈38 m seconds elapsed when height is 38 m above ground≈5.3 seconds
Your answer to part b is correct. That is what you want to graph. So plug in a number of $t$'s, get $h(t)$, and plot them. If I were posing the problem, I would have asked b before a.
Added: c and d are fine, as well. A graph from Alpha is here