Question

Bradley dropped a ball from a roof 16 feet high. Each time the ball hits the ground, it bounces 3/5 the previous height. Find the height the ball will bounce after hitting the ground the fourth time.

Answer 1

2.0736 feet

Explanation:

After the first bounce, the ball rises to a height of ⅗(16) = 9.6.

After the second bounce, the ball rises to a height of ⅗(9.6) = 5.76.

After the third bounce, the ball rises to a height of ⅗(5.76) = 3.456.

After the fourth bounce, the ball rises to a height of ⅗(3.456) = 2.0736.

This can also be modeled as a geometric sequence.

h = 16 (⅗)ⁿ

h = 16 (⅗)⁴

h = 2.0736

Round as needed.