# Homework Help: 2 Ferris wheels

1. Mar 31, 2017

### LaplacianHarmonic

1. The problem statement, all variables
Ferris wheel 1 has constant angular velocity A with radius M described by parametric equations
X=Mcos(At)
Y=Msin(At) + M

Ferris wheel2 has constant angular velocity of B with radius N described by parametric equations
X= Ncos(Bt) + H
Y=Nsin(Bt) + N

At what time are the two point on each Ferris wheel right on top of each other if these two points start at angle 0 for both Ferris wheels?
2. Relevant equations
Parametric equations for the two Ferris wheels

3. The attempt at a solution
When the two points of each Ferris wheel intersect, the x and y coordinates for that point of intersection are the same from each Ferris wheel.

I equated the times for x coordinates of Ferris wheel 1 and Ferris wheel 2.

Help me

2. Mar 31, 2017

### phinds

Yes. Then what? If you don't show any work, there's nothing for us to help you with.

3. Mar 31, 2017

### LaplacianHarmonic

I'm trying to learn how to write in latex properly to show the work.

4. Mar 31, 2017

### LaplacianHarmonic

Can I post a picture of the notebook page and/or dry erase board with the actual work?

5. Mar 31, 2017

### phinds

It's actually against the rules but if it is TOTALLY clear and utterly legible it might pass muster.

6. Apr 2, 2017

7. Apr 2, 2017

### LaplacianHarmonic

A bit difficult to set up the functions to find the time at which both x and y coordinates for the intersection of the two Ferris wheel come out from the 2 sets of parametric equations.

8. Apr 3, 2017

I am stuck

9. Apr 3, 2017

### LaplacianHarmonic

Hello???

10. Apr 3, 2017

### haruspex

How are you interpreting that? What angle? Is this any different from the obvious fact that when t=0 we have At=0 and Bt=0?

Having equations left and right on a page makes it hard to follow the sequence.

I do not understand why you want to work in terms of X and Y, or introduce new labels for radii (they are given).
If the two points coincide at some time t, what two equations can you write involving t?

11. Apr 4, 2017

### LaplacianHarmonic

We use x and y to find the 2 points of intersection.

X1 = R1 [cos (w1 t)] =
R2 [cos (w2 t)] + H

And then solve for t hoping t will match...?

12. Apr 4, 2017

### haruspex

You also have an equation for matching y. Can you manipulate them to eliminate w1?

13. Apr 4, 2017

### LaplacianHarmonic

No.

Y1 = R1 [sin (w1 t)] + R1
= R2 [sin (w2 t)] + R2

14. Apr 4, 2017

### LaplacianHarmonic

w1 does not equal w2

15. Apr 4, 2017

### haruspex

Ok.
Write each equation so that on one side you only have the cos or sine of w1t, and no reference to w1 on the other side. No x or y either.
What algebraic relationship do you know between cosine and sine?

16. Apr 5, 2017

### LaplacianHarmonic

Theta + 2ㅠN = phi

That's interesting

17. Apr 5, 2017

### haruspex

I don't understand. Is that a response to my question about the relationship between the sine of an angle and the cosine of the same angle?
What I'm looking for is equivalent to Pythagoras' Theorem.

18. Apr 6, 2017

### LaplacianHarmonic

This point of intersection at same time is more rare than initially perceived.

It can never occur and almost always occurs once if the conditions aren't perfect.

19. Apr 6, 2017

### haruspex

Perhaps, but let's just concentrate on solving theequations to find out.

20. Apr 7, 2017

### LaplacianHarmonic

The equations are different between intersecting at same number of rotations and intersecting at different number of rotations.