# Thread: Applications of Derivatives help

1. ## Applications of Derivatives help

A Ferris wheel with a 30 ft radius makes one revolution every 10 sec:
a) Assume that the center of the Ferris wheel is located at the point (0,40), and write parametric equations to model its motion.
b)At t=0 the point P on the Ferris wheel is located at (30,40). Find the rate of horizontal movement, and the rate of vertical movement of the point P when t=5sec and t=8 sec.

For a, I think the answer is x=30cost, and y=30sint+40, since the radius is 30ft and it's center is at (0,40), but i think I'm wrong.
For b, I'm not too sure. The concept of horizontal and vertical movement isn't clear to me, especially when t is a value.
Please show work and have the answers, so I won't have to keep guessing, thank you.

A Ferris wheel with a 30 ft radius makes one revolution every 10 sec:
a) Assume that the center of the Ferris wheel is located at the point (0,40), and write parametric equations to model its motion.
b)At t=0 the point P on the Ferris wheel is located at (30,40). Find the rate of horizontal movement, and the rate of vertical movement of the point P when t=5sec and t=8 sec.

For a, I think the answer is x=30cost, and y=30sint+40, since the radius is 30ft and it's center is at (0,40), but i think I'm wrong.
For b, I'm not too sure. The concept of horizontal and vertical movement isn't clear to me, especially when t is a value.
Please show work and have the answers, so I won't have to keep guessing, thank you.
you have to take the angular velocity, $\displaystyle \omega$ , into account ...

$\displaystyle x = 30\cos(\omega t)$

$\displaystyle y = 30\sin(\omega t) + 40$

where $\displaystyle \omega = \frac{2\pi}{10} = \frac{\pi}{5}$

when t = 0 , point P is at x = 30 and y = 40

when t = 2.5, point P should be at the very top of the wheel ... check it.

to find the rates of horizontal and vertical motion, find $\displaystyle \frac{dx}{dt}$ and $\displaystyle \frac{dy}{dt}$ respectively and evaluate them at the requested times.

3. Can you explain to me how W equals pi/5?

$\displaystyle \frac{1 \, revolution}{10 \, seconds} = \frac{2\pi \, radians}{10 \, seconds} =$ ?