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
       
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              *   Vo = 19.6 m/s  *
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