Question

1. Recall the following scenario from a class activity: A ba is thrown (from the ground) to a height of 10 feet. It then falls and bounces repeatedly. After each bounce, it rises to of the previous height (a) Express the total vertical distance the ball travels until it stops (going up and down on each bounce) as a geometric series and compute its value using the short-cut formula for geometric series. Make sure to justify the geometric series you come up with and interpret its value in the context of the ball bouncing. (b) For a ball to bounce to a height of h ft and fall back to the ground, it should take 8Vh seconds Create a formula for how long the kth bounce takes. Determine the limit of this sequence and interpret it in the context of the ball bouncing Use (a) to create a geometric series that represents the total time that the ball is bouncing Evaluate this series using the short-cut formula for geometric series and interpret it in the context of the ball bouncing.

Answer 1

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