Expressing speed with variables

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To calculate the speed of the ball when it hits the floor, consider the energy conservation principles involved in the problem. Initially, the potential energy stored in the compressed spring is converted into kinetic energy as the ball is launched and then into gravitational potential energy as it rises. When the ball reaches its maximum height, its speed can be derived from the initial conditions, factoring in the height H and the gravitational constant g. The final speed just before hitting the floor can be expressed in terms of the variables k, s, m, g, y, and H, focusing on the total mechanical energy conservation. Understanding the underlying physics concepts is crucial for solving the problem effectively.
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Homework Statement


A child's toy consists of a block that attaches to a table with a suction cup, a spring connected to that block, a ball, and a launching ramp. The spring has a spring constant k, the ball has a massm , and the ramp rises a height y above the table, the surface of which is a height H above the floor.

Initially, the spring rests at its equilibrium length. The spring then is compressed a distance s, where the ball is held at rest. The ball is then released, launching it up the ramp. When the ball leaves the launching ramp its velocity vector makes an angle with respect to the horizontal.

Throughout this problem, ignore friction and air resistance.


Homework Equations



The first problem told me to calculate the speed of the ball when it leaves the launching ramp.

I got sqrt((ks^2)-2(mgy))/m
This was correct but on the next problem it is asking me with what speed will the ball hit the floor? All of this is in terms of k,s,m,g,y,or H

I have no idea where to start. My teacher does this to us every week without teaching us a thing
 
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Well, you know m, g, and h right? That should give you a bit to get started on. You shouldn't have to concern yourself with the speed at which it comes off of the inclined plane. You might want to look at more of the theory behind the problem that just the calculations.

hope this helps somewhat
 
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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