A ball is dropped from a height of 12 feet and returns to a height that is one-
half of the height from which it fell. The ball continues to bounce half the
height of the previous bounce each time. How far will the ball have traveled
vertically when it hits the ground for the fifth time? It might be helpful to
sketch the path of the ball.

0.375ft

Step-by-step explanation:

Initial height: 12ft

First bounce: 12/2=12/2¹

Second bounce: (12/2¹)/2=12/2²

Third bounce: (12/2²)/2=12/2³

Fifth bounce: (12/2⁴)/2=12/2⁵

12/2⁵=12/32=0.375ft

explanation:

previous steps have made pa≅ pb ≅ st ≅ su. setting the compass width to ab allows you to make tu the same length. then δstu ≅ δpab by the sss congruence postulate, and ∠p ≅ ∠s by the reason cpctc.