Newton’s Law (F = ma) is actually a stronger statement than the law Newton origi

Question

Newton’s Law (F = ma) is actually a stronger statement than the
law Newton originally wrote down which was that force is the rate
of change of momentum with respect to time: F = d/dt (m(t)v(t)).Here’s something we all know: “Objects fall with an acceleration g = 9.8m/s2 which is independent of their mass.” This assumes that said object has a constant mass. If a falling object gains or loses mass over time things are slightly different. Use this more general form of Newton’s law to solve this: If a raindrop falls from height (starting at zero velocity) and increases in volume at a rate equal to its surface area show that it falls with constant acceleration given by g/4. Hint: It’ll become a first order differential equation. You can assume the density of water is any non-zero number you like.

Explanation / Answer

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