Math (logic and problem solving)
posted by sally on .
a rubber ball is dropped froma building that is 16 meters high. Each time the ball bounces, it bounces up half as high as the previous bounce. It is caught by Romer, the wonder dog, when it bounces 1 meter high. How many meters did the ball travel before it was caught?

height: 16;8;4;2;1
fourth bounce. Distance went 16+2*8+2*4+2*2+1
or another way:
Distance=16+ 16(.5)+16*.5^2+ 16*.5^3+1
this looks like a geometric series, r=.5
So in a geometric series,
an= A_{1}*r^n n=0, 1, 2,..
to find our problem
1=16 (.5)^n
1/16= (1/2)^n
take log base 1/2 of each side..
4=n