# Ferris Wheel Problem using Mathematica

Consider a large Ferris wheel 30 meters in radius and its center stands 80 meters above lake level. At t = 0, a stunt person stands on the top of the Ferris wheel (theta = 0 degrees) 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? Is there only one solution for this set of parameters or are there other angles that would work?

I have worked out this problem numerically and written the equations of motion for the person and the boat. I have also calculated numerically where and when the person lands if he/she steps off the wheel at theta = 0 degrees, theta = 90 degrees, theta = 180 degrees, and theta = 270 degrees. This informed me of the quadrant in which the correct solution occurs.

Could someone assist me in turning this into a mathematica program as I have no experience using it.

Thank You!

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andrevdh
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After some hours reading through mathematica I'm almost done with the code. I would appreciate it if someone could assist me from here... I know the print line will give me a correct angle if i substitute in 314 for n, but I'm not sure why my Catch line is giving its output as 1.

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andrevdh
Homework Helper
Shouldn't it be: (θ[n]) x (180/π) ?
It would have been more natural if you incremented t
and calculated θ, but this would also work.
Does the Catch Throw n (in which case you should maybe Throw[θ[n]]? ) or maybe it outputs true = 1?
Also shouldn't you check for the absolute difference between the two x-coordinates (= 0.5?) (would this give
another possible answer that you have to check for)?

http://reference.wolfram.com/language/ref/Throw.html

http://functions.wolfram.com/

Maybe you should run the loop until the boat has passed the right-hand of the wheel?

Last edited:
I've managed to get an angle now but it is the wrong answer. The (theta[n])(180/pi) does not change if I out a multiplication sign in between. Also I switch the vb and vp around because vp-vb will be -150 for the first term n=1 which is why the output was 1 before. Also I had some sign errors in my Vy0 equation but fixing them still does not yield the proper result. Let me try checking for the absolute difference between vb-vp

Here is my most recent code

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andrevdh
Homework Helper
It seems to me you have to use the Throw[value,tag] format of Throw - see my previous Throw link (expand Details).
You might also consider posting in the Maths or Programming forums.

andrevdh
Homework Helper
My maths indicates that he will land at -38,6 m while the boat will be at -65.03 m at that stage?

I am trying to duplicate your code but am not getting the same result as you; did you update your code recently?

andrevdh
Homework Helper
It seems there might be a solution around 1.92 rad or 110o - see attached file

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