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A green truck is moving to the right. A red truck is moving to the left with a speed of 6 m/s. The mass of the red truck is 1,000 kg and the mass of the green truck is 3,000 kg. How fast must the green truck be moving such that ,if it collides head-on with the red truck and the two trucks stick together, the final velocity of the two trucks is zero

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Answer:

2 m/s

Explanation:

[tex]m_1[/tex] = Mass of red truck = 1000 kg

[tex]m_2[/tex] = Mass of green truck= 3000 kg

[tex]u_1[/tex] = Initial Velocity of red truck = 6 m/s

[tex]u_2[/tex] = Initial Velocity of green truck

[tex]v[/tex] = Velocity with which they move together = 0

For elastic collision

[tex]m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow m_1u_1 + m_2u_2 =0\\\Rightarrow m_1u_1 + m_2u_2 =(m_1 + m_2)v\\\Rightarrow m_1u_1 + m_2u_2 =0\\\Rightarrow u_2=-\frac{m_1u_1}{m_2}\\\Rightarrow u_2=-\frac{1000\times 6}{3000}\\\Rightarrow u_2=-2\ m/s[/tex]

Velocity of the green truck is 2 m/s