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Motion with variable mass

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A spherical raindrop of radius a, falls from rest under gravity. It falls through a stationary cloud so that, because of condensation, its radius increases with time at a constant rate k. Find the distance fallen by the raindrop after time t.

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Solution Preview

A spherical raindrop of radius a, falls from rest under gravity. It falls through a stationary cloud so that, because of condensation, its radius increases with time at a constant rate k. Find the distance fallen by the raindrop after time t

Let the radius of the drop at time t be r

The rate of increase of the radius is given by

As the initial radius is a and it increases ...

Solution Summary

The radius of a raindrop increases as it falls under gravity. The distance covered by the drop is calculated by setting and solving the differential equation. Fully explained.

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