Your sailboat has been running straight course under a light wind at 1 m/sec. Su

Question

Your sailboat has been running straight course under a light wind at 1 m/sec. Suddenly the wind picks up, blowing hard enough to at constant force for 600 N to the sailboat. The only other force acting ton the boat is water resistance proportionality to velocity to the boat. And a proportionality constant for water resistance is b = 100 N-sec/m and the mass of the sailboat is 50 kg, find the quation of the sailboat in motion. And if you have limiting what is the velocity of the sailboat will be in this wind condition

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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