# Using mathematica to solve ferris wheel problem

## 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: 468

DrClaude
Mentor
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.

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];
Print["Jump at ", (\[Theta][nterms]) (180/\[Pi]), \[Degree]]

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

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

DrClaude
Mentor
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.

DrClaude
Mentor
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