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# essay1_solution - Wining the Game Marc Miskin 1...

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Unformatted text preview: Wining the Game Marc Miskin October 24, 2009 1 Introduction In order to determine if my team’s catcher can tag out the runner, we obviously need to know if the catcher will catch the ball before the runner reaches home. That is, is the time it takes the ball to travel from right field to home plate shorter than the time it takes the runner to run home? 1.1 Known • Δ x runner : 20m - The distance between the runner and the home plate as measured at the moment the ball is thrown. • Δ x ball : 65m- The horizontal distance the ball needs to travel to reach home plate from right field. • θ : 30 ◦- The angle (relative to the horizontal) that the ball is thrown at. • v runner : 8.0 m s- The velocity the runner travels at. 1.2 Find • Δ t runner : the time it takes the runner to reach home plate. • Δ t ball : the time it takes the ball to reach home plate. 2 Solution 2.1 Rounding Third: Finding Δ t runner The first piece of information we need to compute is how long it takes the runner to run home. Assuming the runner runs at a constant velocity, the time it takes for him to travel a fixed distance will be given by Δ t runner = Δ x runner v runner So if I release the ball when the runner is 20m from home plate and he is traveling at his maximum velocity of 8.0 m s then he will reach home plate in 20 m 8 ....
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essay1_solution - Wining the Game Marc Miskin 1...

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