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## Homework Statement

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A tennis player strikes an incoming tennis ball of mass m and speed v such that the ball leaves the racket at speed v as well. How much work was done by the tennis player to reverse the direction of the ball? Explain. Did the tennis player do any negative work?

## Homework Equations

##W = Fx = 1/2 mv^2##

## The Attempt at a Solution

Here is my attempt with the use of calculus and differential equations:

##F = ma = mv dv/dx##

##Fdx = mvdv##

Integrating both sides, where the left integral is integrated from 0 to x and the right integral is integrated from v to -v, yielding:

##Fx = 1/2 m(-v)^2 - 1/2mv^2##

##Fx = 1/2mv^2 -1/2mv^2##

##Fx = 0##

Mathematically, it appears that the work done by the tennis player is zero if the magnitude of velocity is equal to that of the starting velocity.

I would assume that this is correct because because work would be greater than zero if the ball leaves the racket at a greater speed than it arrived at the racket and alternatively, work would be negative if the velocity decreased leaving the racket.

I need some clarification with regards to this, any insight would be greatly appreciated.