Two students, sitting on frictionless carts, push against each other. both are initially at rest and the mass of student 1 and the cart is m, and that of student 2 and the cart is 1.5m. if student 1 pushes student 2 so that she recoils with velocity v,  what is the velocity of student 2.

  v₂ = v/1.5= 0.667 v

Explanation:

For this exercise we will use the conservation of the moment, for this we will define a system formed by the two students and the cars, for this isolated system the forces during the contact are internal, therefore the moment conserves.

Initial moment before pushing

    p₀ = 0

Final moment after they have been pushed

    = m₁ v₁ + m₂ v₂

   p₀ =  

   0 = m₁ v₁ + m₂ v₂

   m₁ v₁ = - m₂ v₂

Let's replace

   M (-v) = -1.5M v₂

   v₂ = v / 1.5

  v₂ = 0.667 v

pretty sure it's false