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Mechanics: Vertical projection with air resistance

A particle is projected vertically upward in a constant gravitational field with an initial speed of v_0. Show that if there is a retarding force proportional to the square of the instantaneous speed, the speed of the particle when it returns to the initial position is:

(v_0*v_t)/[(v_0)^2 + (v_t)^2]^1/2

where v_t is the terminal speed.

Please show the frame of reference used and all steps.

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