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