Alice is riding a Ferris wheel which turns at a constant speed

Question

Alice is riding a Ferris wheel which turns at a constant speed. The diameter of the wheel is 16 meters, and it is mounted at a height of 1 meter from the ground. Given that it took 5 seconds for Alice to get halfway up when she was going up on her first round, write an equation for the height of Alice from the ground, H(t) in meters as a function of time t in seconds, where t = 0 represents the time when she started her ride at the lowest point.

Answer 1

So this is a sinusoidal function. If you are starting at the lowest point then I would use a negative cosine function. A negative cosine graph starts at the low point then goes to the midline, the highest point, back to the midline and then the low point to complete one cycle. You can graph y= -(cosx) to visualize this

The graph will be in the form y= -A(b(cos(x-c)) +d

Since the diameter of the wheel is 16 the radius is 8 which is A

To get b you need the period of the function. If it takes 5 seconds to get halfway to the top it would take 10 seconds to get all the way to the top which represents 1/4 of the period so the period is 40 seconds

B= 2pi/p so b = 2pi/40 or pi/20

There is no phase shift so c=o

the vertical shift or midline is at 9 (the wheel is mounted 1 foot off the ground + radius of 8)

Equation is y=-8cos(t x pi/20) +9

Answer 2

Since the diameter is 16m; the height from the top (180°) is 17m minus the height of the seat.

As for height/2; she's 9m high; minus the height of the seat.

s=3rpm

h=st (in rpms)