A ball always bounces to 3/5 of the height from which it is dropped. The ball is dropped from 1.8m and bounces 3 times. How high will it rise from the third bounce?

0.388 m

Step-by-step explanation:

Ok, if the ball is dropped from 1.8 meters, then the height after the first bounce will be 3/5 times 1.8 meters:

h1 = (3/5)*1.8m = 1.08m

now we can think that the ball is dropped from a height of 1.08 meters, then the height after the second rebound will be:

h2 = (3/5)*1.08m = 0.648m

Now, using the same method as before, the height after the third bounce will be:

h3 = (3/5)*0.648m = 0.388 m

Notice that we can write this relation as:

h(n) = 1.8m*(3/5)^n

where n is the number of bounces.

if n = 0 we have the initial height, and if n = 3 we are on the third bounce, then:

h(3) = 1.8m*(3/5)^3 = 0.388 m

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )