a ball is dropeed from a height of six feet and begins bounsing up and down. the height of each bounce is 3/4 the height of the previous bounce. find the total vertical distance traveled by the ball.(HInt- series problem. write a narrative and include the series use with notaion
2007-08-06 07:15:36 · 3 answers · asked by kareena 1 in Science & Mathematics ➔ Mathematics
D = 6+6(2*3/4 +2*3/4^2++++) = 6+ 12*3/4 ( 1/(1-3/4))=42 feet
The ball falls 6 feet and then ups 3/4*6feets and then falls the same distance and so on.That´s the reason of factor 2
The sum of the geometric series is the parenthesis r=3/4
2007-08-06 07:25:45 · answer #1 · answered by santmann2002 7 · 1⤊ 0⤋
The series of (3/4)^n from n =0 to infinity converges to 1/(1 -3/4), since you are starting at six feet, and you go both up and down, 2 times each length, the answer is 6ft(2)(1/(1-3/4)) or 48ft. The only time the length is not doubled is the initial fall, so take 6ft off of this answer, or 42ft.
2007-08-06 14:21:50 · answer #2 · answered by supastremph 6 · 0⤊ 0⤋
technically this could continue on forever.. taking 3/4 of something forever...
(3/4)^n
2007-08-06 14:22:48 · answer #3 · answered by miggitymaggz 5 · 0⤊ 0⤋