A ball is dropped from a height of 8 feet and allowed to bounce. Each time the ball bounces, it bounces back to half its previous height. The vertical distance the ball travels, d, is given by the formula http://schoolisland.com/review/Courses/MasterMath/q3661.gif , where n is the number of bounces. Based on this formula , what is the total vertical distance that the ball has traveled after four bounces?
2007-05-25 07:55:32 · 4 answers · asked by Celia 4 in Science & Mathematics ➔ Mathematics
d = 8 + 16(sum from 1 to 4 of (1/2)^k)
d = 8 + 16(sum((1/2)^1 +(1/2)^2 + (1/2)^3 + (1/2)^4))
d = 8 + 16(sum(1/2 + 1/4 + 1/8 + 1/16))
d = 8 + 16(sum(8/16 + 4/16 + 2/16 + 1/16))
d = 8 +16(15/16)
d = 8 + 15
d = 23 ft
2007-05-25 08:23:55 · answer #1 · answered by T 5 · 0⤊ 0⤋
d = 8 + 16*Summationn (1/2)^k from k = 1 to 4
d = 8 + 16(1/2+1/4+1/8+1/16)
d = 8 + 16(15/16) = 8+15 = 23 feet.
2007-05-25 15:46:26 · answer #2 · answered by ironduke8159 7 · 0⤊ 0⤋
15 3/4 feet in total.
2007-05-25 15:32:52 · answer #3 · answered by cappuccino_lava 6 · 0⤊ 1⤋
put 1 in for K
and then 2 ,3,4
and add the four ans.
2007-05-25 15:11:01 · answer #4 · answered by harry m 6 · 0⤊ 0⤋