Question

can anyone help with this problem?

Let t be the number of seconds that have elapsed since the ferris wheel started. You find that it takes 20 seconds to reach the top of the ferris wheel, which is 56 feet above the ground. The wheel makes one revolution every 60 seconds and the diameter of the wheel is 50 feet.

Write an equation to model the height of your seat above the ground as a function of time.

Answer 1

The top of the ferris wheel is 56 ft above the ground and the diameter of the wheel is 50 ft. this means the ferris wheel is 6ft above the ground.

Answer 2

Ok yea I was actually able to figure that part out. Sorry I should have included that.

Answer 3

Now the function you write will be a cosine or a sine function because the wheel rotates in a circle going up and down al the time

Answer 4

I was also able to figure out that the period is 1200. But I'm not sure if that is helpful with writing the equation.

Answer 5

it makes one full rotation in 60 secs. The period is 60 secs

Answer 6

Ok so do I just plug that into the equation y = a * sin(bx - c)?

Answer 7

Now the diameter of the wheel is 50 ft. and the wheel itself is at 6 ft above ground. So the axis of the curve will be at 31 ft. which is (56 - 6) / 2. This is your amplitude.

So your function is

\[f(x) = A \cos Bx + C\]

Answer 8

or A sin Bx + C.

Answer 9

A and C will be same for both curves but your B and the horizontal transformation varies

Answer 10

C is the position of the Sinusoidal axis the middle points of the curve . Which is at 31 ( (25 + 6) and A = 25 Now all we have is to figure out B.

Answer 11

So if I know the number of cycles is that how I find B?

Answer 12

B = 2pi / 60 and x will be (x-20) so you function will be \[f(x) = 25 \cos [\frac{ \pi }{ 30 }(x-20)] + 31\]