how far does a bouncing ball travel if dropped from a window 16 meters above ground. on each bounce it rises 1/2 the distance of the previous bounce.

Question

A rubber bouncing ball is dropped from a window 16 meters above a sidewalk. On each bounce, it rises half the distance of the previous bounce. The ball is caught when it bounces back up to only one meter form the walk. How far did it travel? explain

Answer 1

Total distance =

 

   16 + (8up + 8down) + (4up + 4down) + (2up + 2down) + 1up

 

= 16 + 16 + 8 + 4 + 1

 

= 45 feet

 

 

Answer 2

On the first drop the ball falls 16 meters.

On the first bounce the ball travels 16 meters (8 meters up and 8 meters down)

On the second bounce the ball travels 8 meters (four up four down)

And so on...

 

The bounces form a geometric sequence:

a_n = a₁(0.5)^n-1

 

The formula for the sum of an infinite geometric series:

S = a₁(1 - r)

S = 16(1 - 0.5)

S = 16(0.5)

S = 8

 

Adding the first drop, the ball travels 24 meters - exactly!