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**1. Homework Statement**

A rocket with a mass M moves along an x axis at the constant speed vi=40 m/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 m1 does it occur?

**2. Homework Equations**

**3. The Attempt at a Solution**

I tried to use the formula v1f=(m1-m2/m1+m2)(v1i)

and I found m2=M-m1 and v1i=40 m/s

And I know that the v1f will equal 20 m/s+v2f

Other than that I don't know how else to proceed. I think I just need a push in the right direction to get the answer, I just don't know where to go next. Thanks!