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Math Help - applied de

  1. #1
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    applied de

    a depth of mass 100 kg is released from a warship into the sea and allowed to sink. While gravity is pulling it down, a buoyancy force of 1/40 times its weight (=mg) is pulling it up. therefore, water resistance also exerts a force on the weapon that is proportional to its velocity, with a constant of proportionality of 10 kg/s. How long will it take for the weight to reach the velocity of 70 m/s?

    i've tried and my de equation is :

    f = ma

    mg-1/40(mg)-10v = m(dv/dt)

    dv/dt = g - (1/40)g - (10/m) v

    dv/dt = (39/40)g - (10/m) v

    v(t) = (39/40)gt - 5(10/m) vt + c

    applying the initial condition (x=0, t=o, v=0) => c=0

    thus v(t) = (39/40)gt - 5(10/m) vt

    is my de is right??? how i get t expression from this equation???


    pls help me....
    Last edited by bobey; March 9th 2010 at 12:08 AM.
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