A ball is dropped from a height of 15 feet. If it rebounds 2/3 of the previous distance, how far does the ball travel vertically?

Question

A ball is dropped from a height of 15 feet. If it rebounds 2/3 of the previous distance, how far does the ball travel vertically?

 

*sequences and series*

Answer 1

Assuming the balls comes to rest:

 

S = a₁ / (1 - r)

 

Now a₁ is the first bounce, 20 ft (10 feet up, 10 feet down.

r is 2/3

 

S = 20 (1 / (1 - 2/3)

S = 20 / (1/3)

S = 60

 

Yet that is only the bounce. The drop of 15 feet must be added.

 

The ball travels (exactly) 75 feet.

Answer 2

A ball is dropped from a height of 15 feet. If it rebounds 2/3 of the previous distance, how far does the ball travel vertically?

 

dropped = 15 ft

rebounds 2/3 (15) ft  = 10 ft

vertical travel = 15 + 10 = 25 ft