Diego drops a ball from different heights. He determines that after each bounce the ball rises to 80% of its previous height. He wants to find out how the total vertical distance that the ball falls before it comes to rest varies with the height from which it dropped.
1. Diego drops the ball from a height of 8 feet and calculates the total vertical distance that the ball falls.
a) Find the vertical distance that the ball has fallen by the third bounce, a1+a2+a3.
b) Is this a converging or diverging series? how do you know?
c) Write a rule and solve for the total vertical distance that the ball falls.

2. Complete the table.
Drop Height (ft): 12, 8, 6, 3, 1
Total Vertical Distance (ft): (calculate)

3. Write an equation to show the relationship between the drop height and the total vertical distance that the ball travels.

Question

Diego drops a ball from different heights. He determines that after each bounce the ball rises to 80% of its previous height. He wants to find out how the total vertical distance that the ball falls before it comes to rest varies with the height from which it dropped.
1. Diego drops the ball from a height of 8 feet and calculates the total vertical distance that the ball falls.
a) Find the vertical distance that the ball has fallen by the third bounce, a1+a2+a3.
b) Is this a converging or diverging series? how do you know?
c) Write a rule and solve for the total vertical distance that the ball falls.

2. Complete the table.
Drop Height (ft): 12, 8, 6, 3, 1
Total Vertical Distance (ft): (calculate)

3. Write an equation to show the relationship between the drop height and the total vertical distance that the ball travels.