# Trigonometry

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. 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.

posted by Reiny

## Similar Questions

1. ### 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
2. ### 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
3. ### physics

A space station, in the form of a wheel 110 m in diameter, rotates to provide an "artificial gravity" of 3.00 m/s2 for persons who walk around on the inner wall of the outer rim. Find the rate of rotation of the wheel (in
4. ### math

a wheel makes 9 3\10 revolutions per minute. if it rotates for 85 minutes . How many revolutions does make ?
5. ### algebra

If a wheel makes 10 5/6 revolutions per minute, how many revolutions will it make if it rotates for 45 minutes?
6. ### math

a wheel makes 8 1/10 revolutions per minute if it rotates for 85 mins. how many revolutions will it make
7. ### algebra

A wheel makes 4 17/20 revolutions per minute. If it rotates for 48 minutes,how many revolutions does it make?
8. ### math

If a flywheel is 3 fee in diameter and if a belt over the wheel is traveling at the rate of 3000 feet per minute, find the number of revolutions of the wheel per minute.
9. ### trig

A ferris wheel with a diameter of 100 feet rotates at a constant rate of 4 revolutions per minute. Let the center of the ferris wheel be at the origin. 1. Each of the ferris wheel's cars travels around a cirlce. a) Write an
10. ### trigonometry

If a flywheel is 3 feet in diameter and if a belt over the wheel is traveling at the rate of 3000 feet per minute, find the number of revolutions of the wheel per minute.

More Similar Questions