A rocket of mass M moves along an x axis at the constant speed vi = 40m/s. A small explosion separates the rocket into a rear section (of mass m1) and a front section; both sections move along the x axis. The relative speed between the rear and front sections is 20 m/s. What are?

(a) The minimum possible value of final speed vf of the front section and

(b) For what limiting value of m1 does it occur?

(c) What is the maximum possible value of vf and

(d) For what limiting value of ml does it occur?