## Analytical Mechanics question

If some dude jumps into the ocean from a 10m diving board so that when he makes contact with the water F=-mg + cv^2 where c is some frictional constant, how do I solve for the velocity of the guy as a function of the depth under water? I am able to integrate so that I obtain velocity as a function of time and then integrate again so that I have the depth under water as a function of time, but I can't seem to get a nice function for velocity in terms of depth. I'm really bad with this stuff so I just thought Id throw the question out there.

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 u can write $$\frac{dv}{dt}=\frac{dx}{dt} * \frac{dv}{dx} = v \frac{dv}{dx}$$