For interest's sake then, let's suppose the two cars collide elastically, conserving both energy and momentum.
Momentum before: 1300*30 - 900*15 kg.m/s =
Momentum after: 1300v1 + 900v2
so 1300v1 + 900v2 = 25500 ...(1)
Kinetic energy before: 1300*302/2 + 900*152/2 = 686250 J
Kinetic energy after: 1300*v12/2 + 900*v22/2
so 1300*v12/2 + 900*v22/2 = 686250 ...(2)
Equations (1) and (2) can now be solved for v1 and v2. (v1 = -75/11 m/s ≈ -6.8 m/s; v2 = 420/11 m/s ≈ 38.2 m/s).
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