Help me find the distance traveled using COR

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To determine the distance traveled by a ceramic ball that bounces on a surface with a coefficient of restitution (COR) that halves after each bounce, one must analyze the motion using the COR formula, which relates the speed of separation to the speed of approach. The ball falls from an initial height, and each bounce reaches a height that is a fraction of the previous height due to the decreasing COR. The distance traveled can be calculated by summing the distances of the fall and the subsequent bounces until the third impact. Understanding the relationship between bounce height and velocity is crucial for solving the problem effectively. The discussion emphasizes the need for a clear approach to calculating the total distance traveled by the ball after three bounces.
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Homework Statement



A ceramic ball of mass m falls form rest a distance h[0] above a horizontal ceramic surface. The subsequent motion of the ball is purely vertical, bouncing ONLY on one spot on the surface. If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.

Homework Equations



COR= speed of separation/speed of approach


The Attempt at a Solution



If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.
 
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corpuzdawn said:

Homework Statement



A ceramic ball of mass m falls form rest a distance h[0] above a horizontal ceramic surface. The subsequent motion of the ball is purely vertical, bouncing ONLY on one spot on the surface. If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.

Homework Equations



COR= speed of separation/speed of approach


The Attempt at a Solution



If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.
Your attempt is just a restatement of the problem, so not really an attempt :frown:

What are your thoughts on how you might approach this problem? For example, how does the height of a bounce depend upon the velocity?
 

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