The speed and direction of the cars after the impact is 5.68 m/s towards the first car.
Given data:
The mass of car is, m = 1300 kg.
The speed of car is, u = 20 m/s.
The mass of another car is, m' = 900 kg.
The speed of another car is, u' = - 15 m/s. (Negative sign shows that direction of car 2 is opposite to car 1)
As per the conservation of linear momentum, "The total momentum of system before the collision must be equal to total momentum after the collision". And this applicable for the perfectly inelastic collision as well. Then the expression is,
[tex]mu+ m'u' = (m+m')v\\\\v=\dfrac{mu+m'u'}{m+m'}[/tex]
Solving as,
[tex]v=\dfrac{(1300 \times 20+(900 \times - 15)}{1300+900}\\\\v = 5.68 \;\rm m/s[/tex]
This will be towards the car 1 ( moving with u = 20 m/s)
Thus, we can conclude that the speed and direction of the cars after
the impact is 5.68 m/s towards the first car.
Learn more about the conservation of linear momentum here:
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