Final answer:
To determine the velocity after collision, the principle of conservation of momentum is used. The total initial momentum is calculated, which is then equal to the momentum of the joined masses post-collision, resulting in a velocity of approximately -0.21 m/s to the left for the combined mass.
Step-by-step explanation:
The question involves a collision in which a 5.0-kg mass moving to the right at 3.0 m/s collides with a 9.0-kg mass moving to the left at 2.0 m/s, and after the collision, the two masses stick together. To find the velocity of the two joined masses after collision, we use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
The momentum of the 5.0-kg mass before collision is (5.0 kg) × (3.0 m/s) = 15.0 kg·m/s to the right, and the momentum of the 9.0-kg mass is (9.0 kg) × (-2.0 m/s) = -18.0 kg·m/s to the left (the negative sign indicates the opposite direction). The total momentum before collision is 15.0 kg·m/s - 18.0 kg·m/s = -3.0 kg·m/s. Since the masses stick together after the collision, their combined mass is (5.0 kg + 9.0 kg) = 14.0 kg.
To find the velocity V after collision, we set the total momentum after the collision equal to the total momentum before the collision: (14.0 kg) × V = -3.0 kg·m/s. Solving for V, we get V = -3.0 kg·m/s / 14.0 kg = -0.2143 m/s. This means the joined masses will move to the left at approximately -0.21 m/s after the collision. Therefore, the correct answer is option 2) -0.21 m/s.