Answer to Question #61883 in Mechanics | Relativity for Abdul

Question

A droplet of perspiration falls off a worker who is standing on a platform 40 m above the
ground. Assume throughout that the drop is spherical (volume of a sphere is equal to 4
3
πr3
while its surface area is equal to 4πr2
). Your objective is to investigate what happens to
the drop as it falls down.
(a) Suppose that as the drop falls, the droplet evaporates at a constant rate. If V is the
volume of the drop, this means that
dV
dt = −c,
where c is a positive constant. Find an expression for dr/dh, that is, the rate of change
of the droplet’s radius with respect to the height h above the ground. (3 marks)
(b) A more realistic model is to suppose instead that the rate of evaporation is proportional
to the surface area of the drop. Find dr/dh now. (3 marks)
(c) Is it possible, in either of these models, that the drop disappears via evaporation just
before hitting the ground?