# Thread: Precalc - Trig help!

1. ## Precalc - Trig help!

Imagine you are riding a 20 meter diameter Ferris wheel that is making three revolutions per minute.
a. What is the linear Velocity?
b. ...angular velocity?
c. There are 8 equally spaced seats on the Ferris wheel, what is the arc length between two adjacent seats?
d. Let H(t) = the height (in meters) at t seconds, where H(0) = 0.
Locate position on Wheel for each time:
0 | 2.5 | 5 | 7.5 | 10 | 12.5 | 15| 17.5 | 20

I'm pretty sure I got a b and c, I just want to check my answers!

2. Originally Posted by Nrp88
Imagine you are riding a 20 meter diameter Ferris wheel that is making three revolutions per minute.
a. What is the linear Velocity?
b. ...angular velocity?
c. There are 8 equally spaced seats on the Ferris wheel, what is the arc length between two adjacent seats?
d. Let H(t) = the height (in meters) at t seconds, where H(0) = 0.
Locate position on Wheel for each time:
0 | 2.5 | 5 | 7.5 | 10 | 12.5 | 15| 17.5 | 20

I'm pretty sure I got a b and c, I just want to check my answers!
You have an angular speed $\omega$. The center of the circle the motion in in is a distance $y_0$ (which is R in this case) above the ground. We can represent this using either the sine or cosine function. I am going to arbitrarily use the cosine function in this instance. We need to have y(t) = 0, so we need to make the phase angle for the cosine function $\pi$ so that we have $R~cos(\omega t + \pi) = -R$. So you know that at time t the vertical component of the position vector is given by
$y(t) = y_0 + R~cos ( \omega t + \pi )$