CAR 1, having a mass of 1,200 kg and traveling with a velocity of 23 m/s due east, has a completely inelastic collision with CAR 2, having a mass of 1,400 kg and a velocity of 28 m/s due west.
In a completely inelastic collision, the two objects undergoing collision are stuck together and, after the collision, move together at the same velocity. Only momentum is conserved in this collision.
The initial momentum of the two cars colliding together was
`M_0 = 1200*23 - 1400*28 `
If the two cars move at a velocity V after collision, the final momentum of the system is `M_1 = (1200+1400)*V`
As `M_0` and `M_1` are equal,
`1200*23 - 1400*28 = (1200+1400)*V`
`V = (1200*23 - 1400*28)/(1200+1400) = ~~-4.46 m/s`
Velocity due east has been considered positive, so the final velocity of the two cars is due west.
The final velocity of the two cars is 4.46 m/s due west.