Re: Geometric Series

[jsc90]

Re: Geometric Series

A ball is dropped from a height of 5 metres. After each bounce, it rises to 60% of its previous height. What is the total vertical distance the ball travels before it comes to rest?

Heres what I did;

a is 5
r is 0.6

S of infinity = a/1-r

my answer came out 12.5m, but the answer is 20m

What am i doing wrong?

 

[pka]

Well, what goes up must come down.
\(\displaystyle 5 + 2(.6)(5) + 2[(.6)^2 (5)] + 2[(.6)^3 (5)] + ...\)

 

[galactus]

What you are doing in a problem like this is adding up two geometric series. One for the trip downward and one for the rebound. The total distance travelled is the sum of these series.

Downward:

5+3+1.8+1.08+0.648............

Upward:

3+1.8+1.08+0.648...............


Let S=the total distance:

\(\displaystyle S=5+2[3+1.8+1.08+0.648...............]

=5+2[3+3(\frac{3}{5})+3(\frac{3}{5})^{2}+3(\frac{3}{5})^{3}............]\)

See what you have to do now?. Use the sum S of the infinite geometric series you

showed in your post. It's all laid out before you.