Question

A Ferris Wheel has a diameter of 56 metres, and one revolution takes 2.5 minutes to complete. Riders may see Niagara Falls if they are highter than 50 metres above the ground.

a) Sketch and label a cycle of the graph that represents the height of the rider above the ground, as a function of time, assuming that the rider gets on at a height of 0.5 metres at the bottom of the Ferris wheel at t=0 minutes.

b) Determine the equation of the function, using h for height and t for time.

c) Are riders able to see the Falls after one minute on the Ferris wheel? Show your solution?

Answer 1

lord i can see why no one wants to do this, but i think we can do it

Answer 2

can u?

Answer 3

i think so

Answer 4

first of it is clearly a trig function right?

Answer 5

yeah

Answer 6

translated up

Answer 7

you know the period is 2.5 and you know the diameter is 56 so the amplitude will be 28

Answer 8

for example
\[28\cos(x)\] goes from 28 to -28

Answer 9

i got it

Answer 10

continue...

Answer 11

you are going to have to use
\[-\cos(x)\] because you want the minimum at t = 0 where cosine is -1

Answer 12

so it is going to look like

\[-28\cos(bx)+c\]

Answer 13

so that is equation?

Answer 14

i would have said
\[c=28\] but that doesn't work because you are .5 up to start, so we can use
\[-28\cos(bx)+28.5\] to insure that we start at .5

Answer 15

then we have to find b

Answer 16

and we know the period is 2.5 minutes, and the formula for the period is
\[\frac{2\pi}{b}=P\]so
\[\frac{2\pi}{b}=2.5\] solve for b and get
\[b=\frac{4\pi}{5}\] check my algebra

Answer 17

so i believe your function should be...
\[-28\cos(\frac{4\pi}{5}x)+28.5\]

Answer 18

how are we doing so far?

Answer 19

yeah i got some ?
i trying to understand
i think u r right
thx

Answer 20

not done yet though

Answer 21

can u solve my next question?

Answer 22

here is a nice graph to show what we got. it looks right
http://www.wolframalpha.com/input/?i=-28cos%284pi+x%2F5%29+%2B+28.5

Answer 23

this graph don't have cycle.

Answer 24

now we have to see how high they are at t = 1, so put t = 1 and find the hight. oh it says write height as a function of t, so you should write
\[h(t)=-28\cos(\frac{4\pi}{5}t)+28.5\]

Answer 25

yes the graph has a cycle. it goes up and down and up and down...

Answer 26

now if we replace t by 1 we get
\[h(1)=-28\cos(\frac{4\pi}{5})+28.5=51.1525...\] from a calculator, so yes, they can see niagra falls
http://www.youtube.com/watch?v=9pQii1L8fGk&feature=related

Answer 27

i got it