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Car A of mass 1200kg traveling at 10m/s , collided in too the back of the car B, which is stationary. Following the collision,. The two cars stick together and travel at 6m/s. What is the mass of a car B?

 May 20, 2021
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Conservation of momentum is the idea here; momentum, the product of mass and velocity, does not change. Since car B is stationary (velocity=0), the momentum before collision is the mass of car A times its velocity, i.e. (1200 kg)(10 m/s). After the collision the cars are moving together at 6 m/s, so the momentum after collision is (1200 kg +\({m}_{B}\)kg)(6m/s), where \({m}_{B}\) is the mass of car B. We need to solve the equation

                                                 \((1200+{m}_{B})(6)=(1200)(10).\)

Distributing and isolating \({m}_{B}\), results in

                                                   \(6{m}_{B}=12000-7200=4800, or \ {m}_{B}=\frac{4800}{6}=800 kg.\)

 May 20, 2021

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