A ball is dropped from a height of $20 m$ If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ___$m$
A ball is dropped from a height of $20 m$ If the coefficient of restitution for the collision between ball and floor is $0.5$, after hitting the floor, the ball rebounds to a height of ___$m$
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Correct Answer: 5
Solution and Explanation
To solve the problem of determining the rebound height of the ball after it hits the floor, we must use the concept of the coefficient of restitution. This coefficient, denoted as e, is defined as the ratio of the relative speed of separation to the relative speed of approach. Here, e is given as 0.5.
The formula for the rebound height h' based on the original drop height h and the coefficient of restitution is:
h' = e2 * h
Substituting the given values:
h' = 0.52 * 20
Calculate the squared coefficient:
0.52 = 0.25
Therefore, the rebound height is:
h' = 0.25 * 20
h' = 5
The calculated rebound height is 5 meters. Confirming with the provided range of 5 to 5, our computed value indeed fits this range.
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