Final answer:
The total momentum before the collision of Car A and Car B is 0.5665 kg·m/s. The total momentum after the collision remains the same due to conservation of momentum. The velocity of the two joined cars after the collision is 0.587 m/s.
Step-by-step explanation:
The total momentum before the collision of Car A and Car B can be found by using the formula:
momentum = mass × velocity.
Given that Car A has a mass of 0.515 kg and moves with a velocity of 1.10 m/s, its momentum is:
0.515 kg × 1.10 m/s = 0.5665 kg·m/s.
Since Car B is at rest, its momentum is 0 kg·m/s.
Therefore, the total momentum before the collision is the sum of the momenta of both cars, which is 0.5665 kg·m/s + 0 kg·m/s = 0.5665 kg·m/s.
To find the total momentum after the collision, we use the conservation of momentum, which states that the total momentum before the collision equals the total momentum after the collision when no external forces act on the system. Since the two cars stick together after the collision, the total momentum remains 0.5665 kg·m/s.
To find the velocity of the two joined cars after the collision, we again use the conservation of momentum. The combined mass of the two cars is 0.515 kg + 0.450 kg = 0.965 kg.
Since momentum is conserved, 0.5665 kg·m/s = 0.965 kg × velocity_after_collision.
Solving for velocity_after_collision gives us velocity_after_collision
= 0.5665 kg·m/s / 0.965 kg = 0.587 m/s.
Therefore, the velocity of the two joined cars after the collision is 0.587 m/s.