A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground.

Question

A ferris wheel is 40 meters in diameter and boarded from a platform that is 1 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answer 1

radius = 20

Imagine the wheel moves from six o'clock position to 8 o'clock. The height as a function of the angle between 6 and 8..., h = f(theta) = [r - r*cos(theta)] + 1 ... you really have to draw this to see...

draw a circle with a radius to 6 and another radius to 8, then draw a line from 8 that is perpendicular to the radius line of 6. r*cos(theta) gives you part of the r that is not part of the height.

so...take away r*cos(theta)-part from r and the 1 is from the base height.

theta as a function of time: (2*pi)/6*t ==> 1 revolution is 2*pi per 6 minutes. this is the rate at which the angle is changing with time.

now sub in pi/3 * t into f(theta) to get f(t) ==> [r - r*cos(pi/3*t)] + 1