A BMW of mass 2.0 x 10 3 kg is traveling at 42 m/s.It approaches a 1.0 x 10 3 kg

Question

A BMW of mass 2.0 x 103 kg is traveling at 42 m/s.It approaches a 1.0 x 103 kg Volkswagen going 25 m/s inthe same direction and strikes it in the rear. Neither driverapplies the brakes. Neglect the relatively small frictionalforces 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 thespeed of the VW after the collision? b) During the collision, which car exerts a larger force onthe other, or are the forces equal in magnitude? Explain. A BMW of mass 2.0 x 103 kg is traveling at 42 m/s.It approaches a 1.0 x 103 kg Volkswagen going 25 m/s inthe same direction and strikes it in the rear. Neither driverapplies the brakes. Neglect the relatively small frictionalforces 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 thespeed of the VW after the collision? b) During the collision, which car exerts a larger force onthe other, or are the forces equal in magnitude? Explain.

Explanation / Answer

Mass of BM W is m = 2000 kg Initila speed of BMW is u = 42 m / s Mass of Volkswagon M = 1000 kg Initial speed of volkswagon U = 25 m / s Speed of the BMW after colliison v = 33 m / s Let the speed of the volkswagon after collision be V from law of conservationof momentum , mu + MU = mv +MV                     84000+ 25000= 66000+ 1000V from this   V = 43 m / s (b). Change in momentum of BMW is P = m ( u-v ) = 18000 kg m / s Change in momentum of the volkswagon P ' = M ( V - U ) = 18000kg m / s P = P ' and time of contact is same . Therefore both cars exerts equal magnitude of force

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