Question

a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing a ball bounces from a height of 2 metres and returns to 80% of its previous height on each bounce. find the total distance travelled by the ball until it stops bouncing @Mathematics

Answer 1

use the sum for geometric series equation

Answer 2

ok.. i know but how do you do that?

Answer 3

sum=18meters

Answer 4

2/(1-0.8) = 2/0.2 = 2*5 = 10m

Answer 5

you use the formula sum to infinity = a / (1 - r) where a = first term (2) and r = commom ratio (0.8)

- as jamesm did.

Answer 6

Here's more detail:
So for the moment ignore the initial drop of 2 m. After that we have pairs up and down.
Find just the down (and then double to account for the up):
with d= 2m (the original height)
we have 0.8d+ 0.8 0.8 d + 0.8 0.8 0.8 d + ...
or d 0.8 (1+0.8+0.8^2 + ...)
the series (with a= 1, r= 0.8) sums to a/(1-r)= 1/(1-.8)= 1/.2= 5
d 0.8 5= 4d= 8m
That's the down. Double it for up and down, 16 m
add the first drop of 2m and finally we get 18m