What Are the Correct Speeds and Masses in These Momentum Problems?

[catala]

Homework Statement

1. 
   An antitank missile (m = 12kg.), when it reaches the maximum height (v = 0) explodes breaking into a large piece of 5kg. and a multitude of small pieces exiting vertically upwards with a speed of 40m / s. What is the speed of the first piece?.

• 
  A locomotive traveling at 20m / s, collides and engages in a car traveling initially in repose after the two at a speed of 16m / s. if the amount of movement of the locomotive-car system is 128kg.m / s. What is the mass of each body?

Homework Equations

\Delta P = I

p = m*v

The Attempt at a Solution

1. \Delta P = mv_f -mv_o = (5 + m)*v - (m*0)

= (5+m)v_f = 5*v_f + m*v_f = 5v + 40*7 \to \boxed{v = -56 m/s}

2. \Delta P = mv_f - mv_o = (m_1 + m_2)16 -20m_1

(m_1 + m_2)16 = 128 \to m_1 = \frac{128 -16m_2}{16}Could you correct my mistakes?

Thanks

 

[xur54]

I looked at the first part:
v=-56 m/s looks like the right answer to me. The variables in the work get mixed up. v becomes vf then goes back to v. Some of the problem might be the starting equation. There should be a summation for the m*vf term because m breaks up into two parts. So you could have m*vf=(m1*v1f+m2*v2f). Then it would help to state that delta P is 0, and you should still get -56 m/s.
Does that help any?

 

[haruspex]

For the second question, you have not arrived at values for m1 and m2.