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Please see attached file for full problem description.

A spherical hailstone falls freely from rest under gravity. It initially has radius a. As it falls its volume increases through condensation at a rate equal to times the surface area, where is a constant.
(a) Show that after a time t its radius r is equal to a+ t.
(b) Show that the velocity v at time t satisfies the differential equation dv/dt = g-3 v/r
(c) Hence show that 4 v=g[a+ t-a^4(a+ t)^-3]