Hard rubber ball is thrown down from a building with a height of 5 metres. After each bounce, the ball rises to 4/5 of its previous height. Total vertical distance d ball has travelled at the moment it hits the ground for the 8th time, to the nearest 10th of a metre, is..____________

I don't get how to solve this.

make a sketch and you will see that the total distances

= 5 + 2(5)(4/5) + 2(5)(4/5)^2 + .... for 8 terms
= 5 + 10(4/5) + 10(4/5)^2 + ... for 8 terms

notice that the first term is not part of the pattern since it does not complete the "up-and-down" path
lets make it fit the patters:
total distance
= (10 + 10(4/5) + 10(4/5)^2 + ... 10(4/5)^7) - 5
= 10 ((4/5)^8 - 1)/(4/5-1) - 5
= 36.6

check:
1st bounce = 5
2nd bounce = 8 , 4 up and 4 down
3rd bounce = 6.4
3rd bounce = 5.12
4th bounce = 4.096
5th bounce = 3.2768
6th bounce = 2.62144
7th bounce = 2.097152
8th bounce = 1.6777216
sum of those 8 terms = 36.611392

A ball with mass 0.15 kg is thrown upward with initial velocity 20 m per sec from a roof of a building 30 m high find the max. height a ball reach?

To solve this problem, we can calculate the total vertical distance traveled by the ball by summing up the distances traveled during each bounce. We know that the height of the building is 5 meters, and after each bounce, the ball rises to 4/5 of its previous height.

Let's break down the problem step by step.

First bounce:
The ball falls from a height of 5 meters and bounces back to 4/5 * 5 = 4 meters.

Second bounce:
The ball falls from a height of 4 meters and bounces back to 4/5 * 4 = 3.2 meters.

Third bounce:
The ball falls from a height of 3.2 meters and bounces back to 4/5 * 3.2 = 2.56 meters.

Fourth bounce:
The ball falls from a height of 2.56 meters and bounces back to 4/5 * 2.56 = 2.048 meters.

Fifth bounce:
The ball falls from a height of 2.048 meters and bounces back to 4/5 * 2.048 = 1.6384 meters.

Sixth bounce:
The ball falls from a height of 1.6384 meters and bounces back to 4/5 * 1.6384 = 1.31072 meters.

Seventh bounce:
The ball falls from a height of 1.31072 meters and bounces back to 4/5 * 1.31072 = 1.048576 meters.

Eighth bounce:
The ball falls from a height of 1.048576 meters and bounces back to 4/5 * 1.048576 = 0.8388608 meters.

To find the total vertical distance traveled by the ball, we need to add up all these distances:

5 + 4 + 3.2 + 2.56 + 2.048 + 1.6384 + 1.31072 + 1.048576 + 0.8388608 ≈ 21.54 meters.

Therefore, the total vertical distance traveled by the ball at the moment it hits the ground for the 8th time is approximately 21.54 meters.