You throw a ball straight up at v_0 (you are on the ground). Derive an expression for the highest point that the ball reaches. Derive an expression for the time it takes to get to the highest point. Derive and expression for the time it takes to come back to you. Be sure you use diagrams and clearly define your coordinate system. All you answers will be symbolic. Show all of your algebra steps. Discuss what forces are acting on the ball after it leaves you hand. Discuss what direction that force is.

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Newton's First Law of Motion

If a very smooth ball is rolled down an inclined surface with zero friction, the ball will continue to roll indefinitely for an infinite time, in an attempt to reach to the same height on the opposite hill!