A sailboat has been running (on a straight course) under a light wind at 1 m/sec

Question

A sailboat has been running (on a straight course) under a light wind at 1 m/sec. Suddenly the wind
picks up, blowing hard enough to apply a constant force for 600 N to the sailboat. The only other
force acting ton the boat is water resistance that is proportional to the velocity of the boat. If the
proportionality constant for water resistance is b = 100 N-sec/m and the mass of the sailboat is 50 kg,
nd the equation of motion of the sailboat. What is the limiting velocity of the sailboat under this
wind?

Explanation / Answer

Ft = Fw - Fd The force of the wind is assumed to be constant: Fw = 600N The drag force is proportional to the velocity Fd = bV Acceleration = net force / mass Which gives you the differential equation of motion: x' = (1/M)(Fw - b x') At the limiting velocity, the net force on the boat is 0, otherwise it would accelerate. Therefore we have: Fw = b Vl

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