Grab the height, h, of your position as a function of time for t for the problem (please show scales on the axes)

Question

a Ferris wheel 30 meters in diameter and bordered from a platform that is 2 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 14 minutes and it turns clockwise. At t=0, you are in the three o'clock position. You then make two complete revolutions and return to the boarding platform.

(a) Graph the height, H, of your position as a function of time t for the problem. Please show on the axes

(b)Find an equation for the height,H,in terms of t

(c) How many minutes later, after t=0, does your height first reach 25 meters above the ground? (Round the answer to two decimal places)

Answer 1

This problem is easier if you draw a diagram with the ferris wheel and the loading platform.

If you are at 3:00 or 9:00 (horizontal from the axis), you are halfway to the top of the ferris wheel.

If you are at 12:00, you are at the top.

If you are at 6:00, you are at the bottom.

Don't forget to add the height from the ground when necessary.

(a) An easy way to do this is to calculate the heights at 12:00, 3:00, 6:00, and 9:00 and 12:00, and draw a curve through them. Don't forget the platform height. You can double-check that the curve is correct by picking a couple of other points.

(b) Google "equation for height of a ferris wheel". t will be a variable. Remember that it takes 14 minutes to complete a full revolution, which is 360 degrees. The height can be expressed with a sine or cosine function.

(c) You can estimate this by looking at your graph from (a), and calculate the exact answer with the equation from (b).