Find the velocity v(t) of a rocket undergoing vertical motion in a medium having

Question

Find the velocity v(t) of a rocket undergoing vertical motion in a medium having a retarding force proportional to the velocity, kmv. Assume that the acceleration of gravity is constant with height and the burn tate of the fuel is constant. Hint: Assume the initial and final values of the velocity to be 0 and v and of the mass m1 and m.

Explanation / Answer

F(net) = -km*v -mg => ma = -km*v -mg => dv/dt = -kv -g => dv/(kv+g) = -dt integrating, we get; ln(kv +g)/k = -t +c at t= 0 , v= 0 => c= ln(g)/k =2.28/k => ln(kv +g)/k = -t +2.28/k v(t) = [e^(-kt +2.28) -g]/k

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