Degrees problem (modelling Ferris wheel)

[fred2028]

So anyways here's my question from my math homework, along with my attempt.

Question:

15) A ferris wheel has a radius of 7 meters. The center of the wheel is 8 meters above the ground. The ferris wheel rotates at a constant speed of 15 degrees/second. The height above the ground of the only red seat can be modelled by the function h(t) = 8 + 7sin(15degrees * t).
b) What is the maximum height of any seat?

And here's my sad answer.

To get from bottom to top, it is 180 degrees. 180/15 = 12 seconds. Plug 12 into equation and you get 8 meters. Doesn't sound right. So I tried starting from 270 degrees, and top is therefore 90 degrees.
Plug 90/15 = 6 seconds, and you get 15 meters, the correct answer.

My question here is, why do you have to start counting the degrees from the positive x-axis? Isn't the lowest point of a ferris wheel at 270 degrees?

 

[Mrspi]

Re: Degrees problem

So anyways here's my question from my math homework, along with my attempt.
Question:

15) A ferris wheel has a radius of 7 meters. The center of the wheel is 8 meters above the ground. The ferris wheel rotates at a constant speed of 15 degrees/second. The height above the ground of the only red seat can be modelled by the function h(t) = 8 + 7sin(15degrees * t).
b) What is the maximum height of any seat?

And here's my sad answer.
[quote:3tkkorl7]
To get from bottom to top, it is 180 degrees. 180/15 = 12 seconds. Plug 12 into equation and you get 8 meters. Doesn't sound right. So I tried starting from 270 degrees, and top is therefore 90 degrees.
Plug 90/15 = 6 seconds, and you get 15 meters, the correct answer.

My question here is, why do you have to start counting the degrees from the positive x-axis? Isn't the lowest point of a ferris wheel at 270 degrees?[/quote:3tkkorl7]

Ok....did you draw a sketch? If the radius of the wheel is 7 m, and the center of the wheel is 8 m above the ground, the "top" of the wheel is 7 m above the center of the wheel, and the center is 8 m from the ground. So, the highest that any seat can reach is 7 m + 8 m, or 15 m from the ground.

Could be that I'm missing something.....

 

[fred2028]

Re: Degrees problem

Ok....did you draw a sketch? If the radius of the wheel is 7 m, and the center of the wheel is 8 m above the ground, the "top" of the wheel is 7 m above the center of the wheel, and the center is 8 m from the ground. So, the highest that any seat can reach is 7 m + 8 m, or 15 m from the ground.

Could be that I'm missing something.....

I know that, but the point of this is for my teacher to see me use periodic functions to find it, not add 7+8. I'm wondering why you always start counting from the positive x-axis when the wheel starts at 270 degrees.

 

[tkhunny]

It is an arbitrary selection of your teacher. It is unnecessary unless otherwise will be marked wrong on an exam. If you can define your periodic function COMPLETELY, it should be acceptable.

Take a look at \(\displaystyle sin(x - \frac{\pi}{2})\), for example. Start it out at x = 0 and see what it does.