Question

A hard rubber ball is dropped from a moving van with a height of 5 metres. The ball rises to 80% of the previous height after each bounce.

a) determine the total vertical distance the ball has traveled when it strikes the ground the eighth time.

b) estimate the total vertical distance the ball travels before it comes to rest.

It's a geometric series, I know this much. My problem comes from the fact that... the initial 5 metres in an anomaly. After the ball hits the ground the first time, it will go up and down the same distance, then up and down 80% less, etc. It's that first 5 that is an odd distance, it only happens once. How would I write the S_n_ formula?

A few ideas I had were:

Sn=/8(1-.8^n)\
\ 1-.8 / +5

Answer 1

Change a to 2a in the formula, and then subtract a from the end to equalize. This resolves the 1/2 distance on the first bounce.

s8=(2a(1-r^n)/(1-r))-a