A rubber ball dropped from a height of exactly 6 ft bounces several times on the floor, loosing 10% of its kinetic energy each bounce. After how many bounces will the ball subsequently not rise above 3 ft
To solve this problem, we can set up an equation to track the height of the ball after each bounce. Let's calculate the height of the ball after each bounce:
After the first bounce, the ball reaches a height of 6 ft * 0.9 = 5.4 ft (losing 10% of its energy).
After the second bounce, the ball reaches a height of 5.4 ft * 0.9 = 4.86 ft.
After the third bounce, the ball reaches a height of 4.86 ft * 0.9 = 4.374 ft.
After the fourth bounce, the ball reaches a height of 4.374 ft * 0.9 = 3.9366 ft.
After the fifth bounce, the ball reaches a height of 3.9366 ft * 0.9 = 3.54294 ft.
From these calculations, we can determine that the ball will subsequently not rise above 3 ft after the ball bounces five times.
.5 = .9*n
log .5 = n log .9
n = log .5 / log .9