Ferris wheel multiple questions

Question

4)  Another Ferris wheel has a radius of 25 feet and reaches a maximum height of 55 feet above the ground. From the location of your seat when the wheel starts turning, it takes you 6 seconds to reach the top. It takes 16 seconds for the wheel to make a full rotation. sketch at graph (you do not need to include it here to turn in it is just to help you write an equation) and then answer the following questions.

a) what is the equation for your graph

b) what do you notice about the amplitude and vertical shift of your graph as they relate to the Ferris Wheel itself?

c) why does your minimum height have to be greater than zero for any Ferris wheel?

Answer 1

To find the height (y) of a seat above the horizontal axis we use the equation y= 25sin(??t). If you looked at the websites you’ll know that the amplitude of a sine wave is the radius of the circle. The period is 16 seconds so ?? = 2??/16 = ??/8 and y = 25sin(??t/8). We start at t=0 y=0, t=4 y=25, t=8 y=0, t=12 y=-25 and t=16 y=0. Note that the minimum value of the height is -25. This means that half of the Ferris Wheel would be above ground and the half would be buried under the ground. So we must shift the minimum value to 5 feet above the ground by adding 30 to our equation.

y=25sin(??t/8) + 30

This new equation now uses ground as a reference so y now represents the height of a seat above ground. Note the location of the starting point. It is neither the top nor the bottom it is 90 degrees CCW from the bottom. To get to the top from here we need 4 seconds but it took you 6 seconds from the current location to get to the top, a time difference of two seconds. Two seconds is 2/16 of a full rotation or 2/16 of 2?? which is ??/4. So we must rotate the seat back ??/4 to account for the two seconds.

y=25sin(??t/8 – ??/4) + 30

Answer 2

Hannah,

 

The information you have given in this problem is inconsistent. If the wheel rotates at a constant rate of motion (uniform circular motion), and it takes 16 seconds to make a full rotation, it would take 8 seconds for a rider to go from the bottom to the top, wouldn't it?

 

I posted a reply to another of your questions similar to this one a short time ago which pointed out the same problem.

 

Maybe I misunderstand, but this a little confusing to me. I could use some clarification on this (if the problem is stated clearly and accurately).