Answer :
Hi there!
We can use the conservation of momentum for an INELASTIC collision:
[tex]m_1v_1 + m_2v_2 = v_f(m_1 + m_2)[/tex]
Let:
m1 = mass of van (5000 kg)
m2 = mass of car (? kg)
v1 = initial velocity of van (10 m/s)
v2 = initial velocity of car (0 m/s)
vf = final velocity of BOTH objects (6 m/s)
We can rearrange and plug in values to solve for m2:
[tex]m_1v_1 + m_2(0) = v_f(m_1 + m_2)\\\\m_1v_1 = v_f(m_1 + m_2)\\\\(5000)(10) = 6(5000 + m_2)[/tex]
Solve:
[tex]50000 = 30000 + 6m_2\\\\20000 = 6m_2\\\\m_2 = 20000/6 = \boxed{3333.33 kg}[/tex]