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Homework Statement:
 A person of mass ##m = 75## kg slides a distance ##d = 5## m on a straight water slide, dropping through a vertical height ##h = 25## m. Determine the mechanical work done by gravity on the person? What is the height h if the mechanical work done by the gravity is ##W = 2010## J?
Relevant Equations:

Probably some of these:
##E = mgh + \frac{1}{2} mv^2##
##W = \Delta \frac{1}{2} mv^2##
I don't really understand if the initial horizontal velocity is 0? Or do I assume it's some constant? Putting aside vertical velocity.
Also how should the "mechanical work done by gravity" be calculated? Is it just ##W = \frac{1}{2}mv^2_{final}  \frac{1}{2}mv^2_{initial}##
Also how should the "mechanical work done by gravity" be calculated? Is it just ##W = \frac{1}{2}mv^2_{final}  \frac{1}{2}mv^2_{initial}##
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