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.
Step by step solution provided.