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Math Help - First-order ODE Word Problem (physics-related)

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    First-order ODE Word Problem (physics-related)

    This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

    Anyway:

    An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.
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    Quote Originally Posted by BlazingFire View Post
    This is for my DE class and I can't seem to figure it out (probably because my physics is a bit rusty).

    Anyway:

    An object of mass 100 kg is released from rest from a boat into the water and allowed to sink. While gravity is pulling the object down, a buoyancy of force 1/40 times the weight (w = mg) of the object is pushing the object up. Also, water resistance exerts a force on the object that is proportional to the velocity of the object, with proportionality constant 10N-sec/m. Find the equation of motion of the object.
    let the downward direction be positive, g = 10 m/s^2 ...

    F_{net} = mg - \frac{mg}{40} - 10v

    m\frac{dv}{dt} = \frac{39}{40}mg - 10v

    \frac{dv}{dt} = 9.75 - 0.1v


    go for it ...
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