Question

A ferris wheel, radius 7.0 takes 32 seconds to make one complete revolution. A rider gets on the ferris wheel 1.0m above ground level.
a) Find a sinusoidal equation for the relationship of height above ground versus time.
b) At what time is the ferris wheel rider 12m above the ground?

Answer 1

remind me . . . by sinusoidal equation you mean one centred around sin(x)?

Answer 2

could be either
sin(x) or cos(x)

Answer 3

Well then would you prefer to start with the height of the Ferris whee riderl at 1m or 8m?

Answer 4

1m

Answer 5

or what do you mean?

Answer 6

well the lowest the rider is on the ferris wheel is 1 m as it is 1 m from above the ground. The highest the rider goes is . . . actually 1 + 2r where r = the radius so 15 m sorry about that

Answer 7

oh, k

Answer 8

I am guessing that your answer is needed in radians?

Answer 9

Let's try to stuff it into this form. Since the man is getting on the Ferris wheel at it's lowest point, it makes sense to use the SINE function, since the sine function starts at 0.
\[\huge y=a \sin (b x)+d\]
a is the amplitude. As whatist pointed out, we can figure out the amplitude based on the radius of the wheel.\[\huge y=7 \sin(bx) + d\]
We also were told that the the man is getting on the wheel 1m above ground level. So our function has been shifted UP one unit.
d represents vertical shift.\[\huge y=7 \sin(bx)+1\]

Answer 10

ok, so how would i find the period?

Answer 11

Hmm, I can't remember.. thinking ^^ lol

Answer 12

k lol

Answer 13

I can't seem to remember how to relate it to time.. that represents the frequency I guess? :o\[\huge \frac{2\pi}{b}=period\]This is how we would find the b value, but I can't, for the life of me, remember how to relate it to the frequency :c lol

Grr sorry beth :3 maybe whatist can help c: hehe

Answer 14

if so then use the format y = a * sin(b*(x-c)) + d
where a = r = radius = 7
b = 2*pi/32 = pi/16
c=8
d=8

Answer 15

I use those number in my graphing calculator and believe I got the graph you are looking for

Answer 16

@zepdrix sin does not start its graph at a minimum but in between a minimum and maximum requiring a horizontal shift c units in length. Also as the amplitude of the sin curve increases it requires more of a shift upwards to have the minimum at one.

Answer 17

Does that help at all?

Answer 18

i dont know, i try graphing it on my calculator but im not getting it for some reason

Answer 19

http://www.wolframalpha.com/input/?i=y+%3D+7+sin%28pi*%28x-8%29%2F16%29+%2B+8

Answer 20

Oh sine starts at 0, but not at it's lowest point :O oh oh good call :3 blah .. my head's not in it today lol

Answer 21

is what im graphing should be \[y=7\sin (8x) +1\]?

Answer 22

nope
click the link I posted I swear it will only lead you to a graph of the values I posted earlier

Answer 23

its because the new minimum of the sin wave after the adjustment by 7 is -7 and we want the minimum to be 1 so to solve for d we go
-7 + d = 1
d = 8

Answer 24

Honestly I am not sure how I got the the c value I was kinda trying to remember how exactly it affected the graph and stumbled on it maybe @zepdrix can help you with that part

Answer 25

I have to go though but I truly do hope I helped you also just remember to close the question when you are finished