A small car (mass = 156.75 kilograms), moving at 115.5 m/s, crashes head on with a 627 kg truck moving at -74.25 m/s in the opposite direction. If the two cars become intertwined and mangled (inelastic), with what velocities does the wreckage move? (include directions)

please explain this to me!! i'm trying to understand this topic and i need some help :/

The collision is inelastic, so the total kinetic energy is not conserved. However, the total momentum before and after the collision is still conserved. So we can write:

[tex]p_i = p_f\\m_1 u_1 + m_2 u_2 = (m_1 + m_2) v[/tex]

where

[tex]m_1 = 156.75 kg[/tex] is the mass of the car

[tex]v_1 = 115.5 m/s[/tex] is the velocity of the car before the collision

[tex]m_2 = 627 kg[/tex] is the mass of the truck

[tex]v_2 = -74.25 m/s[/tex] is the velocity of the truck before the collision

[tex]v=?[/tex] is the velocity of the car+truck after the collision

Re-arranging the equation and substituting the numbers, we find:

[tex]v=\frac{m_1 u_1 + m_2 u_2}{m_1 + m_2}=\frac{(156.75 kg)(115.5 m/s)+(627 kg)(-74.25 m/s)}{156.75 kg+627 kg}=-36.3 m/s[/tex]

And the negative sign means the direction is the same as the original direction of the truck.