Tennis: Fan Height Calculation from Ball Speed

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To determine the height of the fan in a tennis match scenario, the problem involves calculating the potential and kinetic energy of the ball and the fan. The ball bounces upward at 16 m/s, while the fan catches it at 12 m/s. The relevant equations include gravitational potential energy and kinetic energy, suggesting the need to analyze energy conservation. The discussion indicates uncertainty about how to approach the problem, particularly regarding the initial and final energy states. A clear understanding of energy principles is essential for solving the height calculation.
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Homework Statement


In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponents side of the net. If the ball bounces upward from the ground with a speed of 16m/s and is caught by a fan with a speed of 12 m/s, how high above the court is the fan?


Homework Equations


Don't know.


The Attempt at a Solution


How do I start this question?
 
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Start with finding out if there is potential gravitational/spring/kinematic enegery at the beginning or at the end.

mgh_i + .5m(v_i)^2 + .5k(x_i)^2 = mgh_f + .5m(v_f)^2 + .5k(x_f)^2
 
k i'll do that
 

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