a list of data is given for a seat on a ferris wheel that is traveling in a circle. the data is time vs its vertical velocity. the question is to estimate the diameter of the ferris wheel.
The Attempt at a Solution
what i did was integrate the function from 0 to 30 using a reimann sum (which gave me just an approximation because there was no function given...just the vertical velocities every 5 seconds).
i chose o to 30 because at 30 seconds, the vertical velocity became 0 again. this implied to me that the ferris wheel would be at the top because the vertical velocity is 0 at the top.
so i integrated by adding up all the rectangles from 0 to 30 (each with equal base length) and got some value. and since im integrating a velocity function, i should come out with a displacement function for the seat on the ferris wheel.
now my question is, does this value represent the actual distance traveled of the ferris wheel (ie, how far the seat traveled along the circumference) OR does it represent the vertical displacement of the seat (ie, how far it traveled upwards)?
if its the first, then i can find the diameter by doubling that value to get the ful circumference, then setting that equal to (pi)d and getting my diameter.
if its the second, then my answer should automatically be the approximation of the diameter since the vertical displacement from the bottom to the top is the diameter of the ferris wheel.
which one is correct? am i logically justifying it correctly?