Small Raindrop, Big Raindrop

A raindrop initially at rest having a mass of \(0.01 \text{ kg}\) starts to fall towards the center of the earth under its gravitational force. During the fall, the water vapors near it start coalescing uniformly over it, thereby increasing its mass at a constant rate of \(0.005 \text{ kg/s}\).

Find the velocity \((\)in \(\text{ m/s})\) of the raindrop 4 seconds after it starts to fall, to two decimal places.

\(\)
Details and Assumptions:

  • Neglect the effects of air resistance, wind speed, the density of air, or any other atmospheric factor except those stated in the problem.
  • In the duration of this observation, the raindrop is high enough not to hit the ground.
  • Take \(g = 10 \text{ m/s}^2\).
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