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]
