Physics help plz

Question

A student is rushing to class and collides with a vice principal, who was standing still just before the collision. The vice principal has a mass of 100. kg, and the student has a mass of 50. kg, and had a velocity of 2.0m/s before the collision. What is the velocity of the entangled vice principal and student after they collide?

Answer 1

Let m_s = mass of the student and v_s = velocity of the student. Let m_vp = mass of the vice principal and v_vp be the velocity of the vice principal. Let v = velocity of the combined mass of student and vice principal after the collision. Let time 1 be the time just prior to the collision and m2 be the time just after the collision.

Then the total momentum at time 1 is defined as P₁ = m_sv_s + m_vpv_vp = (50)(2) + (100)(0) = 100 kgm/s.

The total momentum at time 2 is defined as P₂ = (m_s + m_vp)v = (50 + 100)v = 150v.

But by the conservation of momentum, P₁ = P₂ therefore m_sv_s + m_vpv_vp = (m_s + m_vp)v or 100 = 150v. Dividing by 150, we get v = 100/150 = 0.67 m/s