# Using mathematica to solve ferris wheel problem

• uxdf700
In summary: No, it works. But I am very surprised that you say that your program works when you tested it with angle 0. As I can see, it doesn't.Would you like me to give you some tips on how to use Mathematica?Yes please.
uxdf700

## Homework Statement

Consider a large Ferris wheel above a lake. The wheel is 30 meters in radius and its center stands 80 meters above the lake level. At t = 0, a stunt person stands on the top of the Ferris wheel (theta=0) which is rotating at a constant angular velocity w = 0.2 rad/s. At t = 0, a rescue boat is 150 m from the vertical center line of the Ferris wheel and travels toward the base of the wheel at a constant speed of 10 m/s.(In other words, if the center of the wheel has coordinates (0, 80) and the initial coordinates of the person are (0, 110), the initial position of the front of the boat is (150, 0)). Assume the person has no initial velocity other than that of the rotating wheel; assume also that there are no sources of friction in this problem. Assume further that the boat is one meter in length and the long axis of the boat is moving directly toward the Ferris wheel. The Ferris wheel is rotating toward the incoming boat.Your program will allow you to determine when should the stunt person step off the Ferris wheel to safely land in the boat as it speeds by. At what angle (with respect to the vertical) should the person step off to accomplish this?

## Homework Equations

http://www.luc.edu/faculty/dslavsk/courses/phys301/classnotes/projectequations.pdf

These are the relevant equations I used to produce my programming code

## The Attempt at a Solution

I have attached my mathematica program. I am getting a result of 240 degrees, however, we are told that the correct angle should be between 90 degrees and 180 degrees. Can anyone help me out here?
Thank you

#### Attachments

• mathematica project 1.PNG
7.8 KB · Views: 564
At the end of the document you link, you have a table with some results. Have you checked that for a given θ on input, you get the correct values using your equations?

It would also be helpful if you pasted your code in a post. It is hard to work with a picture.

DrClaude said:
At the end of the document you link, you have a table with some results. Have you checked that for a given θ on input, you get the correct values using your equations?

It would also be helpful if you pasted your code in a post. It is hard to work with a picture.

I tested the angle zero and I do get the correct values. Here is my code pasted. Thank you for your reply

Clear[g, \[Omega], R, H, h, Vb, \[Theta], Pxo, Pyo, Vxo, Vyo, Ta, Tw, \
Ttotal, Bx, P, nterms]
g = 9.8; \[Omega] = .2; R = 30; H = 80; h = .01; Vb = 10;
\[Theta][n_] := n*h;
Pxo[n_] := Px[n] = R*Sin[\[Theta][n]];
Pyo[n_] := Pyo[n] = H + R*Cos[\[Theta][n]];
Vxo[n_] := Vxo[n] = \[Omega]*R*Cos[\[Theta][n]];
Vyo[n_] := Vyo[n] = -\[Omega]*R*Sin[\[Theta][n]];
Ta[n_] := (Vyo[n] + Sqrt[Vyo[n]^2 + 2*g*Pyo[n]])/g;
Tw[n_] := \[Theta][n]/\[Omega];
Ttotal[n_] := Tw[n] + Ta[n];
Bx[n_] := Bx[n] = 150 - (Vb*Ttotal[n]);
P[n_] := P[n] = Vxo[n]*Ttotal[n] + Pxo[n];
nterms = Catch[Do[If[(Bx[n] - P[n]) < 0, Throw[n]], {n, 1000}];
Throw[0]];
Print["Jump at ", (\[Theta][nterms]) (180/\[Pi]), \[Degree]]

uxdf700 said:
I tested the angle zero and I do get the correct values.
That's not enough. Test for all angles given in the table.

DrClaude said:
That's not enough. Test for all angles given in the table.
I tested the other angles and I am not getting the correct answer. I am having trouble finding the error in my coding

uxdf700 said:
I tested the other angles and I am not getting the correct answer. I am having trouble finding the error in my coding
Which values are incorrect?

The Tair and position of the person P and of the boat Bx at all angles that are not 0.

uxdf700 said:
The Tair and position of the person P and of the boat Bx at all angles that are not 0.
That's strange, because this is not the same thing I got when I tried it. (I don't have access to Mathematica right now).

I can't check if this is the source of the problem, but the way you wrote things is a bit strange. For instance:
P[n_] := P[n] = Vxo[n]*Ttotal[n] + Pxo[n];

Why do you have "P[n]=" after "P[n_] :=" ? I've never seen this in Mathematica, but I'm not a specialist.

I wrote it like this because later on in the code I need to use these functions to define other functions. I don't think it works otherwise

## What is the ferris wheel problem?

The ferris wheel problem is a mathematical problem that involves finding the height, distance, and speed of a passenger on a ferris wheel at a given time. It is a popular problem in introductory physics and calculus courses.

## How can Mathematica be used to solve the ferris wheel problem?

Mathematica is a powerful computational software that can be used to solve complex mathematical problems. It has built-in functions for solving equations, graphing, and performing numerical calculations, making it an ideal tool for solving the ferris wheel problem.

## What are the key variables in the ferris wheel problem?

The key variables in the ferris wheel problem are the radius of the wheel, the angular velocity, and the initial position of the passenger. These variables determine the height, distance, and speed of the passenger at any given time.

## Can Mathematica provide a visual representation of the ferris wheel problem?

Yes, Mathematica has built-in functions for graphing and visualizing mathematical equations. It can generate a graph that shows the position of the passenger on the ferris wheel as a function of time, providing a visual representation of the problem.

## Are there any limitations to using Mathematica to solve the ferris wheel problem?

While Mathematica is a powerful tool, it is only as accurate as the equations and data input by the user. If there are errors in the equations or incorrect data, the results may not be accurate. It is important to double-check all inputs and results to ensure the accuracy of the solution.

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