Please see attached file for full problem description.

A particle whose initial mass is m is projected vertically upwards at time t=0 with speed gT, where T is a constant. At time t its speed is u and its mass has increased to me^(t/T).
a) If the added mass is at rest when it is acquired, show that d/dt(mue^(t/T)) = -mge^(t/T).
b) Deduce that the mass of the particle at its highest point is 2m.
c) If, instead, the added mass is falling with constant speed gT when it is acquired, show the mass of the particle at its highest point is (3/2)m.

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