The ball will reach a height of 21.9375 inches after its fourth bounce.
Each time the ball lands on the ground, energy is lost. The ball deforms on each hit, and part of the kinetic energy is transferred to heat. After each bounce, the ball will become a little bit hotter. When the ball strikes the ground, it will also lose some energy as sound, although this loss will be minimal. similar to how little energy is lost by air resistance.
After the first bounce, the ball reaches a height of 52 inches.
The ball reaches (3/4) of its previous height after every bounce.
After the second bounce, it will reach a height of (3/4) x 52.
After the third bounce, it will reach a height of (3/4) x (3/4) x 52.
After the fourth bounce, it will reach a height of (3/4) x (3/4) x (3/4) x 52.
The height the ball will reach after its fourth bounce is equal to 21.9375 inches.
