Homework Help: Mechanics midterm-terminal velocity question

1. May 13, 2012

Kara-Mustafa

1. A boy is sliding on the water sliding bed. The angle between sliding bed and the horizontal is θ(theta). When the coefficient of the kinetic friction is μ(COF) and when the wate resistance is F(v)=-cv, obtain the terminal velocity. (two frictions - for this i don't know whether it means linear friction+quadratic friction or something else)

3. But anyway, so far I reached this point:

F-force due to gravity
F(v) - force due to water resistance

F*μ+F(v)=mdv/dt

-mgsin(θ)μ-cv=mdv/dt

dt=mdv/mgsin(θ)μ -cv

And I'm stuck right here. Are my workings so far correct? Can you show me how to integrate this function and find terminal velocity. I know it's going to have exponential term which will drop to zero after sufficient time.

2. May 13, 2012

tiny-tim

Welcome to PF!

Hi Kara-Mustafa!Welcome to PF!

You're confusing the friction (µN) with the downhill component of the gravitational force …

you need both