Ferris Wheel Problem using Mathematica

In summary, the conversation discusses a problem where a stunt person needs to safely land in a rescue boat that is approaching a large Ferris wheel. The person is initially standing on top of the wheel, which is rotating at a constant angular velocity, and the boat is approaching at a constant speed. The person has no initial velocity and there is no friction in the problem. The conversation also mentions using Mathematica to solve the problem and determining the correct angle for the person to step off the wheel. There may be other possible solutions and the conversation also mentions checking for the absolute difference between the two x-coordinates. There is some confusion about the use of the Throw function in Mathematica and the possibility of posting in other forums for assistance.
  • #1
Bakir
4
0
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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  • #3
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.
andrevdh said:
 

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  • #4
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:
  • #5
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
 
  • #6
Here is my most recent code
 

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  • #7
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.
 
  • #8
My maths indicates that he will land at -38,6 m while the boat will be at -65.03 m at that stage?
 
  • #9
I am trying to duplicate your code but am not getting the same result as you; did you update your code recently?
 
  • #10
It seems there might be a solution around 1.92 rad or 110o - see attached file
 

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Related to Ferris Wheel Problem using Mathematica

What is the "Ferris Wheel Problem using Mathematica"?

The "Ferris Wheel Problem using Mathematica" is a mathematical problem that involves using the computer software Mathematica to solve a problem related to a Ferris wheel, which is a popular amusement ride.

What is Mathematica?

Mathematica is a software program used for mathematical computations, modeling, and data visualization. It is commonly used by scientists, mathematicians, and engineers to solve complex mathematical problems.

What is the purpose of solving the "Ferris Wheel Problem using Mathematica"?

The purpose of solving this problem is to apply mathematical concepts and use computational tools to model and analyze the motion of a Ferris wheel. This can help us understand the behavior of the ride and make predictions about its movement.

What are the steps involved in solving the "Ferris Wheel Problem using Mathematica"?

The first step is to define the variables and parameters of the problem, such as the radius of the wheel, the height of the passengers, and the speed of the wheel. Then, we use Mathematica to create a mathematical model and solve it using appropriate functions and equations. Finally, we interpret and analyze the results to draw conclusions about the behavior of the Ferris wheel.

What are some real-world applications of the "Ferris Wheel Problem using Mathematica"?

Understanding the motion of a Ferris wheel has practical applications in the fields of engineering and physics. This problem can also be used as a teaching tool to help students visualize and understand mathematical concepts such as circular motion, parametric equations, and differential equations. Additionally, the techniques used to solve this problem can be applied to other real-world problems involving circular motion and oscillation.

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