The height a ball bounces is less than the height of the previous bounce due to friction. The heights of the bounces form a geometric sequence. Suppose a ball is dropped from one meter and rebounds to 95% of the height of the previous bounce. What is the total distance traveled by the ball when it comes to rest?

Question

The height a ball bounces is less than the height of the previous bounce due to friction.  The heights of the bounces form a geometric sequence.  Suppose a ball is dropped from one meter and rebounds to 95% of the height of the previous bounce.  What is the total distance traveled by the ball when it comes to rest?

trantom · Answer

so the series is 1 + 0.95 + 0.9025 ... or 0.95^0, 0.95^1, 0.95^2, ...

trantom · Answer

well you need to figure out how many times the ball bounces

trantom · Answer

thats 0.95^n = 0

trantom · Answer

130 will get you 0.001 or a milimeter, so I think thats sufficient. Now all you have to do is add 0.95^0 + 0.95^1 + 0.95^2 all the way up to 130! just kidding

trantom · Answer

that is what in principal you are doing but I think theres a faster way to do it