Explanation:
Conservation of momentum :
[tex]m_1u_1+m_2u_2=m_1v_1+m_1v_2[/tex]
Where :
[tex]m_1, m_2[/tex] = masses of object collided
[tex]u_1,u_2[/tex] = initial velocity before collision
[tex]v_1,v_2[/tex] = final velocity after collision
We have :
Mass of an engine = [tex]m_1=4M[/tex]
Mass of an car= [tex]m_2=M[/tex]
Initial velocity of railroad engine [tex]m_1=u_1=5 km/h[/tex]
Initial velocity of car [tex]m_2=u_2=0 km/h[/tex] (rest)
Final velocity of railroad engine [tex]m_1=v_1=v[/tex] (same direction )
Final velocity of car [tex]m_2=v_2=v[/tex] (same direction)
[tex]4M\times 5km/h+M(0 km/h)=4Mv+Mv[/tex]
[tex]4\times 5 km/h=5M[/tex]
v = 4 km/h
The speed of the engine and car after they coupled together is 4 km/h.
