Solving for Final Velocities and Min Length of m2

[colmes]

Homework Statement

(Diagram of problem is given in attachment)
m2 is stationary
The coefficient of kinetic friction on m2 is 0.2 while the ground below m2 has a coefficient of friction of 0.

a) Find the final velocity of both objects if m1 moves at the same v as m2

b)Find the minimum length of m2

Homework Equations

mv = p (Momentum)

The Attempt at a Solution

m1v1 = m1v1' + m2v1'
m1v1 = 50v1'
(10)(20) = 50v1'
200/50 = v1'
v1 = 4m/s

I was able to calculate the final velocity of the two objects using conservation of momentum but I have no clue how to calculate the minimum length of m2.

 

[Basic_Physics]

m1 is slowed down from 10 to 4 meters per second on m2 while m2 is speeding up from 0 to 4 m/s. At that point they are moving together.