1. The problem statement, all variables and given/known data A boat weighs 64,000 lb. Its propeller produces a constant thrust of 50,000 lb and the water exerts a resistive force with magnitude proportional to the speed, with k=2000 lb-s/ft. Assuming that the boat starts from rest, find its velocity as a function of time, and find its terminal velocity. 2. Relevant equations F=mg F=ma 3. The attempt at a solution F=mg F=ma m=64000/32=2000 a=2000v/2000=v dv/dt=-g-v dv/dt=-32-v -dv/(32+v)=dt -ln abs(32+v)=t+C ln abs(32+v)=-t+C 32+v=Ce^-t v=Ce^(-t)-32 v(0)=0 C=32 v=32(e^(-t)-1) The answer in the book is v=25(1-e^(-t)); 25 ft/s. So where did I got wrong? Please correct me.