Anthony Smith
12//19/15
Marshall’s Crew
Math
High Dive Write Up Just things to keep in mind:
– The radius of the Ferris wheel is 50 feet
– The center of the Ferris wheel is 65 feet of the ground
– The wheel makes one complete turn every 40 seconds at a counter clockwise direction.
– The cart starts 240 feet to the left of the center (-240)
– The cart travels at 15 feet per second
– The platform he is standing on is at the 3 o’clock positions when the car starts to move
The equation for his height at anytime on the wheel:
65 + [50sin(9T)] = H
65 is the height of the center of the Ferris wheel. 50 feet is the radius and 9t is the angular speed. I take the sine of 9T because sine will give us the height. The Ferris Wheel spins 9 d/s (degrees
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-240 is the starting position of the cart on the x-axis, or 240 feet to the left of the center of the Ferris Wheel. 15 is the constant velocity of the cart. I multiply that by his falling time. Notice that T became W (W= wheel time). W is the time HIs spends on the wheel. That is what I want to find. His falling time is √H/16. For H I plug in the equation I got for the height and then I divide it by the half of gravity, which once again, is 16.
If I find his falling time and the position of the cart I should make that work with his horizontal position so he hits the cart and not the ground. So if I punch that into a calculator I get W = 12.282855 seconds. That is the time he should spend on the wheel and then dive.
To prove this I will try to find the right number for the time which will match with the x-position which is -17.5488. cos (9t) 50 = -17.5488
Then I guessed and checked a few different amount of seconds, I pluged my guess into the place of (t) and kept doing it until I found exactly -17.5488.
(Just say that the time will be over 10 because that is a good number to start