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(10%) Problem 3: A spherical rain drop of radius R and mass Mfalls vertically through a cloud layer. The drop enters the cloud layer at a height H from the ground and exits the cloud at a height h. While inside the cloud the drop accumulates water molecules so that its mass and size grow with time. The mass of the rain drop at time i when inside the cloud is given as follows: m(/) = M+ at with 1 = 0 at the time the drop enters the cloud, and a the rate at which water molecules accumulate. * 25% Part (a) Write an expression for the acceleration in the vertical direction of the raindrop, as a function of time and the velocity v. Choose a coordinate system in which downwards is positive. X Attempts Remain av/t A 25% Part (b) Now take the approximation that the mass gain is much less then the initial mass, so M>> a t. Apply this approximation to this equation. 4 25% Part (c) Integrate this expression from 1 - 0 to 1, where the velocity goes from vo to v, to find the velocity as a function of time. A 25% Part (d) What is the maximum speed the drop can possibly attain?