Answer:
The final velocity of the vehicles will be -75km per hour (leftwards).
Explanation:
Let us call [tex]m_1[/tex], [tex]v_1[/tex] mass and velocity of the truck , [tex]m_2, v_2[/tex] mass and velocity of the car, and [tex]v_f[/tex] the final velocity of the vehicles.
The law of conservation of momentum states that
[tex]m_1v_1-m_2v_2= v_f(m_1+m_2)[/tex]
solving for [tex]v_f[/tex] we get:
[tex]v_f = \dfrac{m_1v_1-m_2v_2}{m_1+m_2}[/tex]
putting in numerical values
[tex]m_1 =300 kg \\v_1 =5km/hr = 1.39m/s\\m_2 = 1000kg\\v_2 = 100km/hr = 27.78m/s[/tex]
[tex]v_f = \dfrac{300*(1.39)-1000*(27.78)}{300+1000}[/tex]
[tex]\boxed{v_f = -21.0m/s }[/tex] (the negative sign indicates that the vehicles are moving in the leftward direction)
or -75.8 km per hour.
