A ball is dropped from a height of 10 m. Each time it strikes the ground it bounces vertically to a height that is 3/4 of the preceding height. Find the total distance the ball will travel if it is assumed to bounce infinitely often.
Answer: 70 m
I cannot for the life of my figure this out.
I tried the obvious way: making the geometric series
and then found the convergence as k --> infinity, and got 40.
Next, because the ball bounces twice, I thought perhaps I needed a 2. I made the following geometric series,
, used the convergence formula, and got 80.
I believe my second attempt makes more sense, but it doesn't equal 70 m.
So, what am I doing wrong?
Thanks!