Question

A ball is dropped from a height of 3m and bounces on the ground. At the top of each bounce, the ball reaches 60% of it's previous height. Calculate the total distance travelled by the ball when it hits the ground the fifth time.

Could you please check over my answer?

Sn= a(r^n-1)
--------
r-1
= 3(0.6^5 -1 )
-----------
0.6-1
= 6.9168

That is the answer i get, but at the back of the book the answer is 10.8m. Can you correct what im doing wrong? TIA

Answer 1

first fall 3
second up and fall=2*3*.6=3.6
third up and fall= 2*3*.6^2=2.16
fourth up and fall=2*3*.6^3=you do it
and that agrees with the book.

Answer 2

look at my work. Notice the 2 in it? Did your think that the distance was up and down?

If you start on the ground, go up to 3 and back down, you can use your formula but subtracting the initial three upwards.

Sn=6(.6^4-1)/(.6-1) -3
= you do it
Notice you only repeat it four times, it hits the ground at the end of the fourth bounce. Think about that. THe first bounce it starts the first repetition and ends on the sound bounce, and so on.

Answer 3

but is there any way i can apply that to the formula given?