A ball is dropped from rest at the top of a 6

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A ball is dropped from rest at the top of a 6.10 m tall building, falls straight downward, collides inelastically with the ground, and bounces back. The ball loses 10.0% of its kinetic energy every time it collides with the ground. How many bounces can the ball make and still reach a windowsill that is 2.44 m above the ground?

Let's consider the process for the ball leaves the building to just before hit the ground. The energy is conserved for this process, that is, the initial potential energy is equal to the kinetic energy before the ball hits the ground.

, where h0 is the height of the building.
Then the tall hits the ground and bounces back, just after it bounces back, its kinetic energy is 90% of the original one, or 0.9Ek1. Then the ball reaches the highest point, the kinetic energy is 0, the process follows conservation of energy again, that is , where h1 is the height of the ball bounces back the first time.

So

Then the tall falls and hits the ground and bounces back again.

So the nth time the ball bounces back, the height is

So the 8th bounce the ball still makes the high 2.44 m.