Car 1 has a mass of 3kg and is moving to the right with a velocity of 5m/s. Car 2 has a mass of 2kg and is moving to the left towards Car 1 with a velocity of -3 m/s. Car 1 collides with car 2. After car 1 collides with car 2. Car 1 bounces back towards the left with a velocity of -1.4 m/s. What is the momentum of car 2? What is the velocity of car 2?

Explanation:

Let us say cart A has 4kg mass and 5m/s velocity and running at rarr  direction.

Cart B has 3kg mass and 4m/s velocity running at larr  direction.

Let us assume once they stick the combination runs at rarr  direction with a velocity of V. The mass of the combination would be (4+3) = 7kg.

Momentum of masses before stick

= rarr(4xx5)+larr(3xx4)

= rarr(20-12)

= rarr 8

Momentum of the masses after stick

= rarr(7xxV)

= rarr 7V

It is given that the carts are travelling on a frictionless track. Also here we have to assume that at the moment of sticking there is no energy loss by noise or vibration or heat.

Assuming the above conditions we can say that final momentum is equal to initial momentum.

momentum before stick = momentum after stick

rarr 8 = rarr 7V

     V = rarr (8/7)

    V = rarr 1.17m/s

So the final velocity of the system would be 1.17m/s at the initial direction of the 4kg mass.

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