(10%) Problem 3: A spherical rain drop of radius R and mass M falls vertically through a cloud layer. The drop enters th

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10 Problem 3 A Spherical Rain Drop Of Radius R And Mass M Falls Vertically Through A Cloud Layer The Drop Enters Th 1 (33.14 KiB) Viewed 53 times

(10%) Problem 3: A spherical rain drop of radius R and mass M falls 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 when inside the cloud is given as follows: m() = M + ar 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 . Choose a coordinate system in which downwards is positive. 25% Part (b) Now take the approximation that the mass gain is much less then the initial mass, so M>>at. Apply this approximation to this equation. * 25% Part (e) Integrate this expression from t = 0 to I, where the velocity goes from vo to v, to find the velocity as a function of time. (0) VBt * Attempt Remain 25% Part (d) What is the maximum speed the drop can possibly attain?