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A police car has a mass of 1,200 kg and is moving 21 m/s east when it is hit behind by a van going 30 m/s in the same direction. After the collision, the police car’s velocity changes to 32 m/s east while the van continues at 27 m/s east. What is the mass of the van?

Answer :

Given that the mass of the car is M = 1200 kg.

The initial velocity of the car is u_M = 21 m/s

The final velocity of the car is v_M = 32 m/s

Let the mass of the van be m.

The initial velocity of the van is u_m = 30 m/s

The final velocity of the van is v_m = 27 m/s

We have to find the mass of the van.

According to the conservation of momentum,

[tex]Mu_M+mu_m=Mv_M+mv_m_{}[/tex]

Substituting the values, the mass of the van will be

[tex]\begin{gathered} 1200\times21+m\times30=1200\times32+m\times27 \\ 25200+30m=38400+27m_{} \\ 30m-27m=38400-25200 \\ 3m=13200 \\ m=4400\text{ kg} \end{gathered}[/tex]

Thus, the mass of the van is 4400 kg.

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