Calculating Projectile Speed in Terms of k, s, m, g, y, and H

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To calculate the speed of a ball when it leaves the launching ramp, one must express it in terms of variables such as k, s, m, g, y, and H. The discussion emphasizes using conservation of mechanical energy, although the presence of friction complicates the calculations. Participants suggest breaking the problem into three parts to better understand the dynamics involved. The initial speed at the bottom of the ramp can be determined by considering forces, including friction and gravity, affecting the ball's motion. Ultimately, a clear approach to the problem is essential for deriving the correct expressions for both launch and impact speeds.
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Calculate vr, the speed of the ball when it leaves the launching ramp. Express the speed of the ball in terms of k, s, m, g, y, and/or H.

i know it will contain m, y and k

also

With what speed will the ball hit the floor? Express the speed of the ball in terms of k, s, m, g, y, and/or H.

i am so confused when it comes to creating these "expressions" i don't even know where to begin or what the heck to do.
 

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I would use conservation of mechanical energy, of course if there wasn't friction, is the system frictionless?
 
it says nothing about friciton
 
Well imagining there's friction, you could calculate the forces to calculate the initial speed at the bottom of the ram, then friction and gravity will slow down the ball til it hits the top, then just use projectile motion.
 
see, that just blew over my head, I am still boggled
 
Divide the problem into 3 parts.
 
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Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .

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