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....