Tennis ball bouncing on the floor - How high does it bounce?

AI Thread Summary
A tennis ball released from a height of 4.6 meters bounces three times, losing 21% of its energy with each bounce due to heating. To determine the height of the bounce after the third impact, the initial potential energy must be calculated, which requires the weight of the ball. The discussion highlights the challenge of applying mechanical energy concepts without complete information. The focus is on understanding energy loss and its effect on bounce height. Ultimately, solving the problem involves calculating the remaining energy after each bounce to find the final height.
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Homework Statement



A tennis ball bounces on the floor three times. If each time it loses 21% of its energy due to heating, how high does it bounce after the third time, provided we released it 4.6 from the floor?


Homework Equations





The Attempt at a Solution



I just can't deal with energy. Do I have to make use of mechanical energy?
 
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Did you find how much energy it was released with i.e. the energy of the ball 4.6(m?) above the ground.
 
I'd need to know the weight of the ball to do that, and all I'm given is how much energy the ball loses due to heat after each bounce, and how high the ball is when I throw it.
 
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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