Proving an equation

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Homework Statement



Ball with mass m is connected by a strong string of length L to a pivot point and held in place in a vertical position. A wind exerting constant force of magnitude F is blowing from left to right. If the ball is released from rest, show that the maximum height H it reaches (the vertical displacement), as measured from its initial height, is:

H = 2L / 1 + (mg/F)2



Homework Equations



Work and energy related equations.


The Attempt at a Solution


I did dimensional analysis of the final equation but I ended up with something other than [L], which is the unit for height.
As for starting...
Does finding the work of the wind have anything to do with it?
I'm not sure where to start from.
 

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