Problem solving?!

Question

Suppose you drop a ball from 1 meter above the floor. Each time the ball hits the floor after falling from a height of h meters, it rebounds to a height of 0.8h. (So you drop it from 1 meter, it hits the floor, it rebounds to 0.8 meters, falls to the floor, rebounds to (0.8) (0.8) = 0.8^2 meters, etc.) Find the total distance the ball travels up and down.

Answer 1

The ball will travel an infinite distance since the function that describes the balls motion, distance traveled = h₁(.8) + h₂(.8) + h₃(.8) ... approaches 0 but never reaches this value.

 

Since we never reach a value of 0, the ball will never stop bouncing, although the height that the ball will bounce will be infinitesimally small as time approaches ∞⁺.

 

Hope this helped.

 

Keith Isles Messmer