Question

i am having difficulties figuring this out....

a ball has dropped from a height of 15m and bounces 60% of the previous height. the total distance ball travels after the 9th bounce is...

i got this equation done but i do not know how to calculate this to find the answer

15(0.6^9-1)/0.6-1

could you show me how to do it?

Answer 1

the trick here is that the first bounce has a different pattern than the following bounces

distance of 1st bounce = 15 ,...... just down
distance of 2nd bounce = 2(15)(.6) , ..... up and down
distance of 3rd bounce = 2(15)(.6^2)
distance of 4th bounce = 2(15(.6^3)
...
distance of 9th bounce = 2(15)(.6^8)
so total distance
= 15 + 8 terms
= 15 + 2(15)(.6) [ (.6^8 - 1)/(.6 - 1)]

I get 59.24

check my arithmetic