3.14** Consider a rocket subject to a linear resistive force, f = -bv, but no other external forces. Use Equation (3.29) in Problem 3.11 to show that if the rocket starts from rest and ejects mass at a constant rate k = -m, then its speed is given by k U = - Vex b 1- ( ) "]. SECTION 3.3 The Center of Mass 3.15 * Find the position of the center of mass of three particles lying in the xy plane at r, = (1, 1, 0), r2 = (1, -1, 0), and r3 = (0, 0, 0), if m, = my and my = 10m ]. Illustrate your answer with a sketch and comment.mi: = aim\" + Fe\". (3.29) Review the derivation of Equation (3.6) but keep the external force term] 01) Specialize to the ease of . rocket taking off vertically (from rest) in a gravitational eld 3, so the equation of motion becomes mi: = mu\" 4 mg. (3.30)