Final answer:
Using the principle of conservation of momentum, we can find the velocity of car B after the collision with car A moving 0.888 m/s east. The velocity of car B after the collision is 4.740 m/s east.
Step-by-step explanation:
In this problem, we have two cars colliding. Car A has a mass of 331 kg and is moving east at 3.87 m/s, while car B is stationary and has a mass of 208 kg. After the collision, car A moves 0.888 m/s east. We need to find the velocity of car B after the collision.
To solve this problem, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision.
Before the collision, the momentum of car A is given by:
P(A) = m(A) * v(A)
Substituting the values, we have:
P(A) = (331 kg) * (3.87 m/s) = 1280.97 kg m/s
Since car B is stationary, its initial momentum is zero.
After the collision, the momentum of car A is given by:
P(A') = m(A) * v(A')
Substituting the values, we have:
P(A') = (331 kg) * (0.888 m/s) = 294.408 kg m/s
Since the total momentum before the collision should be equal to the total momentum after the collision, we can write:
P(A) + P(B) = P(A') + P(B')
Since car B is initially stationary, its initial momentum is zero. So we can simplify the equation to:
P(A) = P(A') + P(B')
Substituting the values, we have:
280.97 kg m/s = 294.408 kg m/s + P(B')
Solving for P(B'), we find:
P(B') = 1280.97 kg m/s - 294.408 kg m/s = 986.562 kg m/s
Finally, we can find the velocity of car B after the collision by dividing P(B') by the mass of car B:
v(B') = P(B') / m(B)
Substituting the values, we have:
v(B') = 986.562 kg m/s / 208 kg = 4.740 m/s
Therefore, the velocity of car B after the collision is 4.740 m/s east.