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8. A car of mass 3,000 kg, moving at a speed of 20 m/s, is overtaking a truck of mass 7,500 kg, moving at a speed of 16 m/s in the same direction and sense. What is the velocity of the center of mass of the system formed by the car and the truck?

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MathPhysidn

Answer:

17.1 m/s

Explanation:

The velocity of the center of mass is the weighted average of each object's velocity. For two objects, m₁ and m₂, with velocities v₁ and v₂, the center of mass moves with velocity:

[tex]\LARGE \text {$ v_{cm}=\ $} \huge \text {$ \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} $}[/tex]

In this case, the car has a mass of 3000 kg and a velocity of 20 m/s. The truck has a mass of 7500 kg and a velocity of 16 m/s. Since both vehicles are moving in the same direction, both velocities have the same sign. The velocity of the center of mass is:

[tex]\LARGE \text {$ v_{cm}=\ $} \huge \text {$ \frac{(3000\ kg) (20\ m/s) + (7500\ kg) (16\ m/s)}{3000\ kg + 7500\ kg} $}\\\\\LARGE \text {$ v_{cm}=\ $} \huge \text {$ \frac{180,000\ kg\ m/s}{10,500\ kg} $}\\\\\LARGE \text {$ v_{cm}=17.1\ m/s $}[/tex]

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