Unless otherwise stated, in the following problems we assume that the gravitational force is constant with g = 9.81 m/sec2 in the MKS system and g = 32 ft/sec2 in the U.S. Customary System.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 of 600 N to the sailboat. The only other force acting on 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, find the equation of motion of the sailboat. What is the limiting velocity of the sailboat under this wind?
Solution Step 1 Here it is given that there are two forces acting on a sailboat1. Constant horizontal force due to the wind 2. Force due to water resistance opposing the motion of sailboat Also we can see that all the motions are along the horizontal axis. Step 2 Force due to the wind = 600NLet initial velocity be u By Newton’s second law of motion 50Using the integrating constant Now integrating both sides