Question

Need help with Parametric Equation problem involving a Ferris Wheel!!! Help!!

Answer 1

post the problem and I'll give it a look

Answer 2

thank you..A Ferris wheel with an 18-foot radius and center 22 feet above the ground is turning at one revolution per minute. Suppose that on a coordinate system, the ground surface is represented by the x-axis and the center of the wheel is on the y-axis.
a) Assume you board the Ferris wheel at its lowest point at t=0 minutes. If the Ferris wheel goes around 4 times, at what values of t will you reach your maximum height?
b) Write a pair of parametric equations that models the coordinates (x,y) of a seat on the rotating Ferris wheel. The equations should be in terms of x,y, and t where x and y are in feet and t is time in minutes.
c) According to the modeling you wrote in part b, is the Ferris wheel rotating clockwise or counter-clockwise? Explain your answer.

Answer 3

a is easy!
it's b and c

Answer 4

in general you know that we will have to convert
\[x \to r \cos \theta\]\[y \to r \sin \theta\]and it looks like we will be using the formula for a circlewith center (22,0)\[ (x-22)^2+y^2=r^2\]

Answer 5

now we just need to get theta in terms of t and do the substitution

Answer 6

ok

Answer 7

ok

Answer 8

can you get theta in terms of t?

Answer 9

i dunno

Answer 10

it makes a revolution of 2pi radians in 1 minute, so how can we write theta as a function of t when t is in minutes?

Answer 11

i am helping my daughter with this..so this is Greek to me!

Answer 12

she has an awful teacher!!!!!!!!!!!!1

Answer 13

I see...
well the answer is\[\theta=2\pi t\]and we know that \[r=18\]so we have \[(x-22)^2+y^2=18^2\]\[x\to 18\cos(2\pi t)\]\[y\to18\sin(2\pi t)\]so substitute in those formulas for x and y into the equation above and it will be in terms of t.

Answer 14

so that is b?

Answer 15

once you do the substitution, yes
that is a pain to write out though, just tell your daughter to sub what's above for x and y into the equation for the circle that is directly above it

Answer 16

I don;t see how you found a easy if you could not find that \[\theta=2\pi t\], so what do you have for a anyways?

Answer 17

a is 30 seconds.1.5 min 2.5 min, 3.5 min

Answer 18

yes?

Answer 19

no formula required

Answer 20

true, I guess you can just see that...

Answer 21

thank you!

Answer 22

can i ask one more? difft problem? but should be quick

Answer 23

sure try me :)

Answer 24

thanks..Simultaneous modeling the motion of two boats. Suppose the Lady Anna begins at 1 p.m. from a harbor .4 nautical miles north of Charlotte Rose's start location, traveling due east at 10 knots. One pair of parametric equations for this motion are XingT=10T and YT=.4. Display the path (on your graphing calculator). Unclear how she does this.

Answer 25

sorry..4th line equation should be XT=10T

Answer 26

are you sure it's not x=10t
?

Answer 27

well there is a small T next to the X

Answer 28

like\[xt=10t\]or \[x_t=10t\]
???

Answer 29

more like the latter but not exactly

Answer 30

i'd assume that..

Answer 31

pretty sure it's supposed to be the latter, otherwise the equation says that Lady Anna doesn't move...

Answer 32

ok..let's go with that..

Answer 33

this is a strange question
all I can see to do is put the graphing calculator into parametric mode and plug in \[X_t=10t \]\[Y_t=0.4\]which gives you a very silly looking graph.

Answer 34

just looks like this:

Answer 35

ok..we graphed it..does seem strange..but generally two parallel lines

Answer 36

only one line actually represents the motion, the one I have with the arrow, the other is the x-axis

Answer 37

as t increases positively so does x...
that's it

Answer 38

in that problem..(of course there is another question)...it asks...what is the time of day when T=0

Answer 39

which is 1:00 p.m.

Answer 40

right

Answer 41

then it asks..what value of T would represent Noon, the time the Charlotte Rose leaves anchorage. I say it is -1 . My daughter says 0

Answer 42

This is silly, the question says nothing about anchorage that I see o-0
I agree her teacher is probably pretty bad. The problem just says
"Suppose the Lady Anna begins at 1 p.m. from a harbor .4 nautical miles north of Charlotte Rose's start location, traveling due east at 10 knots"
there is no formula for Charlotte moving, just that she sits there.
I suppose t=-1 would be how you represent noon given what we have, but it seems like the question is a bit incoherent...

Answer 43

ok..i agree.

Answer 44

this really doesn't make any sense because t is based on the formula we have
x=10t
so t=-1 makes no sense (or at least does not apply to our equations) because we don't know what the ships motion was before 1pm.

Answer 45

but it is the only option...

Answer 46

at t=0 the formula says Lady what's-her-face is at y=0.4, so the answer cannot be that for noon t=0 as well

Answer 47

LAST question (promise) for this same one...USE YOUR DISPLAY to decide which boat travels 50 nm first. Where is the other boat when the first boat has gone 50 nm? Make and test the changes.