With each bounce off the floor, a tennis ball loses 18% of its mechanical energy due to friction. When the ball is released from a height of 2.9 m above the floor, what height will it reach after the fourth bounce?

170 cm

130 mm

130 cm

13 cm

130 cm

Explanation:

After each bounce, the mechanical energy decreases by 18%, which means the maximum height decreases by 18%. Modeling this as exponential decay:

h = 290 (1 - 0.18) ⁿ

h = 290 (0.82) ⁿ

h = 290 (0.82) ⁴

h = 130

The ball reaches a height of 130 cm.