Question

A BMW of mass 2000 kg is traveling at 42 m/s. It approaches a 1000 kg Volkswagen going 25 m/s in the same direction and strikes it in the rear. Neither driver applies the brakes. Ignore the relatively small force on the cars due to the road and due to air resistance. (a) If the collision slows the BMW down to 33 m/s, what is the speed of the VW after the collision? (b) During the collision, which car exerts a larger force on the other, or are the forces equal in magnitude? Explain.

(a) 43 m/s (b) consult Newtons' laws and/or the ideas of conservation of momentum for your explanation.

The answer to part a is posted with the question, I don't know how to explain part b

Answer 1

Part b)

Here Newton's 2nd law states that the rate of change of momentum gives us the force applied on the body so that this will gives us a condition of impulse momentum conservation also which tells that if the impact of timing of collision is same for both the cars are same so that ,

Ft = Pf- Pi

Which means if the collisions timing is same then the change in momentum will give us the force exerted by the car on another car,

So here for BMW

F(BMW) = 2000(-9) = -18000 N

For VW

F(VW) = 1000(9) = 18000 N

Here magnitude of the forces are equal so that we can say that the forces are equal in magnitude for both the cars here.