Final answer:
The total momentum of the two cars before the collision is calculated by adding the individual momenta of Car A and Car B. The velocity of the joint cars after impact can be found by setting the total momentum before and after the collision equal to each other. The common velocity of the joint cars after impact is found to be 58.08 m/s.
Step-by-step explanation:
(i) To calculate the total momentum of the two cars before the collision, we can use the formula:
momentum = mass x velocity
Car A has a mass of 120 kg and a velocity of 200 km/h, which is equivalent to 200,000 m/3600 s = 55.56 m/s. Therefore, the momentum of Car A is 120 kg x 55.56 m/s = 6667.2 kg·m/s.
Similarly, Car B has a mass of 100 kg and a velocity of 220 km/h, which is equivalent to 220,000 m/3600 s = 61.11 m/s. Therefore, the momentum of Car B is 100 kg x 61.11 m/s = 6111 kg·m/s.
Adding the momenta of Car A and Car B, we get the total momentum before the collision: 6667.2 kg·m/s + 6111 kg·m/s = 12,778.2 kg·m/s.
(ii) To calculate the velocity of the joint cars after the collision, we can use the principle of conservation of momentum. Since the collision is assumed to be perfectly inelastic, the total momentum before the collision is the same as the total momentum after the collision.
Let's assume the common velocity of the joint cars after impact is V. Using the same formula as above, the total momentum after the collision is (120 kg + 100 kg) x V.
Setting the two total momenta equal to each other:
12,778.2 kg·m/s = (120 kg + 100 kg) x V
220 kg x V = 12,778.2 kg·m/s
V = 12,778.2 kg·m/s / 220 kg
V = 58.08 m/s
Therefore, the velocity of the joint cars after impact is 58.08 m/s.