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Math10

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## Homework Statement

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.

## Homework Equations

F=mg

F=ma

## 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.