CATAGORY: Mechanics QUESTION: A tennis ball is thrown from ground level with velocity Vo directed 30 degrees above the horizontal. If it takes the ball 1.0 second to reach the top of its trajectory, what is the magnitude of the initial velocity?

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The initial vertical component of velocity is (1) Vy,o = Vo sin(30) As the ball rises gravity slows the ball down until the vertical velocity is zero. The equation that describes the vertical component of velocity as a function of time is (2) Vy = Vy,o - gt Where g = 9.8m/s^2 is the magnitude of the acceleration due to gravity and t is time. Now when t = 1s Vy = 0 (this corresponds to the maximum height) so we have. (3) 0 = Vy,o -g(1s) Substituting (1) and g = 9.8m/s^2 into (3) gives (4) 0 = Vo sin(30) - 9.8 m/s solving for Vo (5) Vo = (9.8 m/s)/ sin(30) = (9.8 m/s)/ 0.5 = 19.6 m/s ******************** * * * Vo = 19.6 m/s * * * ********************

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