Final answer:
The velocity of the center of mass for the two 3 kg masses with given velocities is 3î - 1.5j m/s.
Step-by-step explanation:
To find the velocity of the center of mass for two masses with velocities, we use the formula:
Velocity of center of mass (Vcm) = (m1v1 + m2v2) / (m1 + m2)
Given the masses m1 = m2 = 3 kg and velocities v1 = 2î + 3j m/s and v2 = 4î - 6j m/s, we plug these values into the formula:
Vcm = (3 kg * (2î + 3j) + 3 kg * (4î - 6j)) / (3 kg + 3 kg)
This simplifies to:
Vcm = ((6î + 9j) + (12î - 18j)) / 6 kg
Vcm = (18î - 9j) / 6 kg
Vcm = 3î - 1.5j m/s
Therefore, the center of mass velocity for the system is 3î - 1.5j m/s.