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DIRECTIONS: Please write complete, concise responses to the following problems. Show all relevant work on any calculations, and be sure to explain what you are doing. Please staple this sheet to the top of your work. 1. Geometric Series: A certain ball has the property that each time it falls from a given height, it rebounds to 80% of its previous height. If we assume that air resistance is negligible, the total distance the ball travels during all of its bounces will involve sums of geometric series. Assuming that the ball is dropped from a height of 10 feet, find this total vertical distance traveled, keeping in mind that the ball doesn't just travel downward; it travels upward as well. We can also calculate total time. In general, the time (T) it takes for a ball to reach the ground, for any bounce, from a height (H) satisfies the relationship T = 14 . V7 . How long does it take for the ball in this problem to stop bouncing? Remember to keep in mind the total time for both upward and downward movement (Use g = 32ft/s])