Question

A hamster enters a wheel at the lowest point and begins to run . The height of point R (in the diagram below) above the ground is given by the function ℎ(𝑡) = −17.5 cos ( 2pi/3 𝑡) + 19, where ℎ is height in centimeters and 𝑡 is time in seconds where 𝑡 => 0. c.

How long does it take the wheel to make 4 full rotations? State your answer using exact values

Answer 1

also how would i figure out the radius for the wheel?

Answer 2

period = 2π/k
in our case k = 2π/3
period = 2π/(2π/3)
= 3

so one rotation takes 3 seconds, thus 4 rotations would take 12 seconds

The radius of the wheel would be the amplitude of your cosine curve which is 17.5 cm

Here is a graph of your courve:

http://www.wolframalpha.com/input/?i=y+%3D+%E2%88%9217.5cos(2%CF%80%2F3x)+%2B+19