A ball is dropped from rest at the top of a 6.10 m tall building,falls straight

Question

A ball is dropped from rest at the top of a 6.10 m tall building,falls straight downward, collides inelastically with the ground andbounces back. The ball loses 10.0% of its kinetic energyevery time it collides with the ground. How many bounces canthe ball make and still reach a window sill that is 2.44m above theground?
answer: 8 bounces

Explanation / Answer

for the first time falling down, the ball has velocity when reachedto the ground=v1conservation of energy m*g*6.1=m*v12/2=>v1=10.93 m/s after the first bounce: velocity of the ball v1':v1'2=0.9*v12=>v1'=k*v1=>v2'=k2*v1 ; k=0.9 the height that the ball can reached after each bounce h=vi'2/2g=(ki*v1)2/(2g); i th bounces h=2.44 => ki=0.632 => i˜8.7 => i=8(i is interger)

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