A car with a mass of 1380 Kg is traveling at 23 m/s to the north. A truck with a mass of 1625 Kg is traveling at 26 m/s to the south. Imagine that both of these vehicles crash into each other head-on and get stuck together. What will their velocity be immediately after the collision

This problem can be solved by the Conservation of Momentum principle which establishes the initial momentum [tex]p_{i}[/tex] must be equal to the final momentum [tex]p_{f}[/tex], and taking into account this is aninelastic collision:

Before the collision:

[tex]p_{i}=mV_{o}+MU_{o}[/tex] (1)

After the collision:

[tex]p_{f}=(m+M)V_{f}[/tex] (2)

Where:

[tex]m=1380 kg[/tex] is the mass of the car

[tex]V_{o}=23 m/s[/tex] is the velocity of the car, directed to the north

[tex]M=1625 kg[/tex] is the mass of the truck

[tex]U_{o}=-26 m/s[/tex] is the velocity of the truck, directed to the south

[tex]V_{f}[/tex] is the final velocity of both the car and the truck

[tex]p_{i}=p_{f}[/tex] (3)

[tex]mV_{o}+MU_{o}=(m+M)V_{f}[/tex] (4)

Isolating [tex]V_{f}[/tex]:

[tex]V_{f}=\frac{mV_{o}+MU_{o}}{m+M}[/tex] (5)

[tex]V_{f}=\frac{(1380 kg)(23 m/s)+(1625 kg)(-26 m/s)}{1380 kg+1625 kg}[/tex] (6)

Finally:

[tex]V_{f}=-3.49 m/s[/tex] The negative sign indicates the direction of the velocity is to the south