# Trigonometry

posted by Anonymous

The diameter of the wheel is 165 ft, it rotates at 1.5 revolutions per minute, and the bottom of the wheel is 9 ft above the ground. Find an equation that gives a passenger's height above the ground at any time t during the ride. Assume the passenger starts the ride at the bottom of the wheel.

1. Reiny

1.5 revs -- 60 sec
1 rev --- 40 seconds

So the period is 40 seconds

2π/k = 40
k = π/20

amplitude = 165/2 = 82.5

height = 82.5 sin (π/20)t, where t is in seconds
But that would give us a min of 82.5, and we want to have a min of 9
so height = 82.5 sin (π/20)t + 91.5

But we know that for t = 0 , we should get 9
so we have to apply a phase shift

let height = 82.5 sin (π/20)(t + c) + 91.5
when t = 0, height = 9
9 = 82.5 sin(π/20)(t+c) + 91.5
-1 = sin (π/20)(c)
we know sin 3π/2) = -1
so (π/20)(c) = 3π/2
c/20 = 3/2
c = 30

height = 82.5 sin (π/20)(t+30) + 91.5

checking:
at t = 0 we should get height = 9 , we do!
at t = 10 we should get 91.5 , we do!
at t= 20 , we should get a max of 174 , we do!
at t = 30, we should get 91.5 again, we do!
at t = 40 we should be back to 9, we do!

This is just one such equation, we could have used a cosine function in a similar method.

## Similar Questions

1. ### Math

The rim of the London Eye (a 135m diameter ferris wheel) moves 26 cm/sec, slow enough for passengers to safely get on the wheel from the platform (2 meters above ground level) without stopping the wheel at the bottom of its rotation. …
2. ### Trigonometry

The diameter of the wheel is 165 feet, it rotates at 1.5 revolutions per minute, and the bottom of the wheel is 9 feet above the ground. Find an equation that gives a passenger's height above the ground at any time t during the ride. …
3. ### Trigonometry

My answer: Y= -82.5 cos (4pi/3)x+91.5 (Period: 1.5=2pi/b --> b= 4pi/3 ) The diameter of the wheel is 165 feet, it rotates at 1.5 revolutions per minute, and the bottom of the wheel is 9 feet above the ground. Find an equation that …
4. ### Calc

Suppose that after you are loaded into a Ferris wheel car, the wheel begins turning at 3 revolutions per second. The wheel has diameter 14 meters and the bottom seat of the wheel is 1 meter above the ground. Express the height h of …
5. ### trigonometry

a ferris wheel is 50 meters in diameter with the bottom of the wheel 1 meter off the ground it makes a full revolution in 12 minutes. What function would track the height above the ground for a point that is at the bottom of the wheel …

A ferris wheel has a radius of 13 m. It rotates once every 24 seconds. A passenger gets on at the bottom of the wheel from a ramp which is one metre above ground level. a) If the height of the passenger is measured from the ground, …