If a ball is initially dropped from height h and has coefficient of restitution 0.9 .How many bounced will the ball make before comping to rest? Please help...
1 Answer
See below
Explanation:
If the ball was dropped from a height
#U = m g h# .
So, just before it's first collision with ground, the ball will have kinetic energy
#T = mgh #
The Coefficient of Restitution,
In the reference frame of ground, only the ball has Kinetic Energy.
And so
So:
# h_1 = 0.81 h_o #
Follows that:

# h_2 = 0.81 h_1 = 0.81^2 h_o # 
# h_3 = 0.81 h_2 = 0.81^3 h_o # 
# ... # 
# h_n = 0.81^n h_o #
In this highly idealised model, the ball will never come to rest, ie