Determine the equation of motion of the object


An object of mass 2 kg is released from rest from the platform 30 m above the water and allowed to fall under the affect of gravity. After the object strikes the water, it begins to sink with gravity pulling down and buoyancy force pushing up. Suppose that the force of gravity is constant, no change in momentum takes place on impact with the water, the buoyancy force is 1/2 the weight (weight = mg), and the force due to air resistance or water resistance is proportional to the velocity, with proportionality constant b1 = 10 N-sec/m in the air and b2 = 100 N-sec/m in the water. Determine the equation of motion of the object. What is the velocity of the object 1 min after it is released?

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Mathematics: Determine the equation of motion of the object
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