A 1200 kg car is traveling 21.1 m/s. It collides with a stationary car of mass 1500 kg, and the two vehicles lock together. What is the speed of the combined cars immediately after the collision?

A) 7.5 m/s

B) 16.5 m/s

C) 9.4 m/s

D) 11.8 m/s

Answer:

C) 9.4 m/s

Explanation:

[tex]m_1[/tex] = Mass of moving car = 1200 kg

[tex]u_1[/tex] = Initial velocity of moving car = 21.1 m/s

[tex]m_2[/tex] = Mass of stationary car = 1500 kg

[tex]u_2[/tex] = Initial velocity of stationary car = 0

v = Velocity of the combined cars

As the momentum in the system is conserved we have

[tex]m_1u_1+m_2u_2=(m_1+m_2)v\\\Rightarrow v=\dfrac{m_1u_1+m_2u_2}{m_1+m_2}\\\Rightarrow v=\dfrac{1200\times 21.1+1500\times0}{1200+1500}\\\Rightarrow v=9.378\approx 9.4\ \text{m/s}[/tex]

The velocity of the combined mass is 9.4 m/s.

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