Final answer:
The magnitude of the momentum of the system is 12 kg·m/s, the direction is to the left (negative x-axis), and the total kinetic energy of the system is 264 J.
Step-by-step explanation:
To find the magnitude of the momentum of the system, we must consider both masses and their respective velocities. First, we calculate the momentum of each object using the formula p = m × v, and then add them vectorially since momentum is a vector quantity.
For the 9.0 kg mass moving at 4.0 m/s:
p1 = (9.0 kg) × (4.0 m/s) = 36 kg·m/s
For the 6.0 kg mass moving at 8.0 m/s:
p2 = (6.0 kg) × (8.0 m/s) = 48 kg·m/s
Since the 6.0 kg mass is moving in the opposite direction (negative x-axis), its momentum is negative. We combine the momenta:
Total momentum (p_total) = p1 + (-p2) = 36 kg·m/s - 48 kg·m/s = -12 kg·m/s
The negative sign indicates that the direction of the momentum of the system is to the left.
To calculate the total kinetic energy of the system, we use the kinetic energy formula KE = ½ m v^2 for each mass and then sum them up:
KE1 = ½ (9.0 kg) × (4.0 m/s)^2 = 72 J
KE2 = ½ (6.0 kg) × (8.0 m/s)^2 = 192 J
Total kinetic energy (KE_total) = KE1 + KE2 = 72 J + 192 J = 264 J