Ball into cup off ramp, need to derive equation

AI Thread Summary
The discussion focuses on deriving an equation to determine the distance a ball must be placed on a ramp at a 40-degree angle to land in a cup positioned 10 cm above the ground. The table height is 0.73 meters, and the ball has a mass of 3.6 grams, with 30% of its energy lost during motion. The user is struggling to integrate various physics equations, including kinematic equations and energy considerations, to find the correct distance. There is confusion about the problem's requirements and the calculations involved, leading to frustration over the inability to progress. Clarification on the equation derivation process and any additional insights would be beneficial.
nawor
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Homework Statement


The problem is to find at what distance the ball has to be placed at on a ramp given a certain angle measurement of said ramp. The cup's position will be given a few minutes prior to testing so there are more unknown variables.
Table Height: .73M
Cup Height: 10cm
Angle measurement is 40 degrees
Ball Mass: 3.6 grams
.3: rotational, so we are supposed to only use 70% of the energy calculated
We are required to derive an equation to use at the spot to figure out how far up the ball needs to be (given the cup distance)


Homework Equations


X=(1/2) A*T^2+ViT+Xi
V= sq root (2gh)
D=RT
V=AT+Vi
A=V/T1
F=MA


The Attempt at a Solution


Ive used the X=... equation and entered the square root equation into it, but i still cannot figure out how to derive it. I've figured out the sin/cos which is .6428 and .7660 (I would just multiply then to get distance).
Any hints would be greatly appreciated. If I've left anything out or forgot to mention some key element, please state that.
 
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Um, what is the question, exactly? What you've written is very confusing.
 
I apologize for not being concise and coherent. But I need to derive an equation so that when I put in the location of the cup, I can figure out how far up the ball should go on the ramp. The ramp is 40 degrees, height of table is .73m, height of the cup is 10 cm or .1m, and the mass of the ball is 3.6grams. We are only supposed to use 70% of the energy calculated because 30% is lost when the ball is moving/rolling. I can show some more of my work but I haven't progressed, I continue to get an identity...which is becoming very frustrating. I don't know If i am explaining it any better.
 
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