Calculating Time and Speed of Rebounds with Coefficient of Restitution

AI Thread Summary
The discussion focuses on calculating the time taken for a ball to rebound after being dropped, considering the coefficient of restitution (e) and the effects of gravity (g). The initial rebound height is determined by the equation h = x^2/(2g), where x is the rebound speed. There is a debate about the correct application of the quadratic formula to find the time taken to reach the rebound height, with concerns raised about dimensional consistency. Participants also inquire about the speed of the ball upon its second impact and the subsequent rebound speed. The conversation emphasizes the need for accurate calculations in understanding the ball's motion and rebound behavior.
Darth Vader
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Homework Statement


I drop a ball downwards vertically onto a smooth table. The coefficient of restitution is 0<e<1. The ball rebounds upwards vertically with speed x. What is the time taken between the time that the ball was dropped to its nth rebound?

Also, what is the time taken before the ball becomes stationary?

Homework Equations


e = speed of separation/speed of approach
Constant acceleration formulae

The Attempt at a Solution


Say the ball rises to a height h after the first rebound. Then h = x^2/(2g). The time taken to reach this height is t = x/g using the quadratic formula...
 
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Darth Vader said:
Say the ball rises to a height h after the first rebound. Then h = x^2/(2g).
Yes.
Darth Vader said:
The time taken to reach this height is t = x/g using the quadratic formula...
That cannot be right because the right hand side has dimension time-squared.

With what speed does it hit the floor the second time? What will be the next rebound speed?
 

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