Sandra is riding the Ferris wheel, and her height can be modeled by the equation H(t) = 25 cospi over 14t + 31, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Sandra before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Sandra begins the ride at the top, how far from the ground is the edge of the Ferris wheel when Sandra's height above the ground reaches a minimum?

You must show all work.

Question

Sandra is riding the Ferris wheel, and her height can be modeled by the equation H(t) = 25 cospi over 14t + 31, where H represents the height of the person above the ground in feet at t seconds.

Part 1: How far above the ground is Sandra before the ride begins?
Part 2: How long does the Ferris wheel take to make one complete revolution?
Part 3: Assuming Sandra begins the ride at the top, how far from the ground is the edge of the Ferris wheel when Sandra's height above the ground reaches a minimum?

You must show all work.

anonymous · Answer

Part 1: Since the range of a cosine function is between -1 and 1. So the lowest point would be (-1*25) + 31 = 6 feet

anonymous · Answer

ok now where didi the t go or are we trying to find t

anonymous · Answer

Part 2: The B value is pi/14 in this equation. Since B = 1 cycle of a cosine wave/time to complete on cycle. Since one cycle of a cosine wave is 2pi and the B value is pi/14, the time is (2pi)/(pi/14) = 28 seconds.

$$f(t)=Acos(Bt +C) + D$$

anonymous · Answer

OK, I misread the part 1 question. Since she is starting the ride at t=0 then the cos(0) =1
So (1*25) + 31 = 56 feet.

anonymous · Answer

Part 3: Since the cosine is minimum at -1, then (-1*25) +31 = 6 feet.