1. The problem statement, all variables and given/known data When an object is submersed in a liquid, it experiences a buoyant force equal to the weight of the liquid displaced by the object. As an object moves through a liquid, there is a resistive force which is directly proportional to the density of the liquid, the cross sectional area A of the object (perpendicular to the direction of motion) and the square of the speed v of the object. A spherical object of mass m and density λ > 1000 begins to sink in a pool of water of depth D. Set up the differential equation with initial condition for the depth of the object below the surface of the water. Use 1000 kilograms per cubic meter as the density of water. 2. Relevant equations N/A 3. The attempt at a solution I am choosing the downward direction (y-direction) to be positive. The object starts at the origin and descends to a depth D. We consider three forces, all in the y-direction: the weight of the spherical object, the buoyant force (= weight of the water displaced by the sphere), and the resistive force. I use Newton's 2nd law: ΣFy = may = mobject(d2D/dt2) = Fobject - Fbuoyant - Fresistive = mobjectg - (1000 kg/m3)(4*πr3/3)g - kλπr2(dD/dt)2, (where k is just a constant of proportionality) and my initial condition would be D(0) = 0 Would this be correct? edit: Added g for the buoyant force.