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
also how would i figure out the radius for the wheel?
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
To find out how long it takes the wheel to make 4 full rotations, we need to determine the time it takes for the height to repeat itself 4 times.
Since the height of the point R is given by the function ℎ(𝑡) = −17.5 cos ( 2π/3 𝑡) + 19, we can see that the height variation is due to the cosine function.
The cosine function has a period of 2π, meaning it repeats itself every 2π units of time. Since we want to find the time for 4 full rotations, we need to multiply the period by 4.
Therefore, the time it takes for 4 full rotations is:
Time = 4 * Period
Time = 4 * 2π
Time = 8π
So, it takes 8π seconds for the wheel to make 4 full rotations.