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.

Answer 1

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?

Answer 2

Part 1:
At t = 0 is when the ride begins.
H(0) = 25cos(0) + 31 = 25 + 31 = 56 feet

Part 2:
When the wheel makes one complete revolution, Sandra will be at her original height when the ride started(56 feet).
H(t) = 25*cos((pi/14)t) + 31 = 56
cos((pi/14)t) = 1
(pi/14)t = 2pi => t = 28 seconds

Part 3:
Minimum occurs when t = 14 seconds. The height at the time will be H(14) = 31 - 25 = 6 feet

Answer 3

Ya, I found that but I don't know if the first part is correct. Can you explain?

Answer 4

@Hero @jim_thompson5910 @myininaya

Answer 5

@wio

Answer 6

does aric200's answer make sense?

Answer 7

for the first part, he just plugged in t = 0 and evaluated

H(t) = 25*cos( (pi/14)*t ) + 31

H(0) = 25*cos( (pi/14)*0 ) + 31

H(0) = 25*cos( 0 ) + 31

H(0) = 25*1 + 31

H(0) = 25 + 31

H(0) = 56

Answer 8

What about the second part? Specifically, (pi/14)t = 2pi => t = 28 seconds

Answer 9

well I would do it a different way (but you get the same answer)

In general, y = A*cos(Bt - C) + D has a period of T = 2pi/B

So...

T = 2pi/B

T = 2pi/(pi/14)

T = 2pi*(14/pi)

T = 28pi/pi

T = 28


So the period of this function is 28 seconds. It will take 28 seconds to do a complete revolution.

Answer 10

Ok this was very helpful. Thank you.

Answer 11

you're welcome