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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!
(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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