Final answer:
The total momentum of the system is 24.10 kg·m/s at an angle of 48.4 degrees north of east.
Step-by-step explanation:
To find the total momentum of the system, we need to consider the momentum of each ball separately and then add them together. Momentum is calculated as the product of mass and velocity.
The momentum of the 4.00 kg ball moving at 4.00 m/s to the east is 4.00 kg * 4.00 m/s = 16.00 kg·m/s to the east.
The momentum of the 6.00 kg ball moving at 3.00 m/s to the north is 6.00 kg * 3.00 m/s = 18.00 kg·m/s to the north.
Adding these two momenta together, we get a total momentum of 16.00 kg·m/s to the east + 18.00 kg·m/s to the north.
Using the Pythagorean theorem, we can find the magnitude of the total momentum:
Magnitude = sqrt((16.00 kg·m/s)^2 + (18.00 kg·m/s)^2) = sqrt(256.00 kg^2·m^2/s^2 + 324.00 kg^2·m^2/s^2) = sqrt(580.00 kg^2·m^2/s^2) = 24.10 kg·m/s.
To find the direction of the total momentum, we can use trigonometry. The angle can be found using the tangent function:
Angle = arctan(18.00 kg·m/s / 16.00 kg·m/s) = arctan(1.125) = 48.4 degrees north of east.