A 480 kg car moving at 14.4 m/s hits from behind another car moving at 13.3 m/s in the same direction. If the second car has a mass of 570 kg and a new speed of 17.9 m/s, what is the velocity of the first car after the collision?

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Question:

A 480 kg car moving at 14.4 m/s hits from behind another car moving at 13.3 m/s in the same direction. If the second car has a mass of 570 kg and a new speed of 17.9 m/s, what is the velocity of the first car after the collision?

Answers

Answer:Velocity of the first car after the collision, [tex]v_1=8.93\ m/s[/tex]Explanation:It is given that,Mass of the car, [tex]m_1 = 480\ kg[/tex]Initial speed of the car, [tex]u_1 = 14.4\ m/s[/tex]    Mass of another car, [tex]m_2 = 570\ kg[/tex]Initial speed of the second car, [tex]u_2 = 13.3\ m/s[/tex]  New speed of the second car, [tex]v_2 = 17.9\ m/s[/tex]  Let [tex]v_1[/tex] is the final speed of the first car after the collision. The total momentum of the system remains conserved, Using the conservation of momentum to find it as :[tex]m_1u_1+m_2u_2=m_1v_1+m_2v_2[/tex][tex]m_1u_1+m_2u_2-m_2v_2=m_1v_1[/tex][tex]480\times 14.4+570\times 13.3-570\times 17.9=480v_1[/tex][tex]v_1=8.93\ m/s[/tex]So, the velocity of the first car after the collision is 8.93 m/s. Hence, this is the required solution.

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