Chapter 2, Problem 2.12P

A particle is projected vertically upward in a constant gravitational field with an initial speed υ₀. 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

$\frac{{\upsilon }_0{\upsilon }_t}{\sqrt{{\upsilon }_0^2+{\upsilon }_t^2}}$

where υ_t, is the terminal speed.