Final answer:
Applying the conservation of momentum to the collision, the green car's velocity after the collision is calculated to be -2.5 m/s. However, since this velocity is not an option provided in the question, and the closest one is 1.0 m/s to the left, there seems to be a discrepancy that needs clarification.
Step-by-step explanation:
The problem describes a collision between two toy cars with different masses moving in opposite directions. According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. We apply this principle to find the velocity of the green car post-collision.
First, we calculate the total momentum before the collision:
Momentum of green car = (mass of green car) x (velocity of green car) = 12.0 kg x (-4 m/s) = -48 kg·m/s.
Momentum of blue car = (mass of blue car) x (velocity of blue car) = 6.0 kg x (+2 m/s) = +12 kg·m/s.
Total initial momentum = -48 kg·m/s + 12 kg·m/s = -36 kg·m/s.
Next, we calculate the momentum of the blue car after the collision and find the momentum of the green car:
Momentum of blue car after collision = (mass of blue car) x (velocity of blue car after collision) = 6.0 kg x (-1 m/s) = -6 kg·m/s.
Let the final velocity of the green car be V. Then:
Momentum of green car after collision = (mass of green car) x (final velocity of green car) = 12.0 kg x V.
According to the conservation of momentum:
Total initial momentum = Total final momentum
-36 kg·m/s = -6 kg·m/s + 12.0 kg x V
-36 kg·m/s + 6 kg·m/s = 12.0 kg x V
-30 kg·m/s = 12.0 kg x V
V = -30 kg·m/s / 12.0 kg
V = -2.5 m/s.
However, the options given in the question (A to D) do not include -2.5 m/s. If we assume a small typing error and consider that the options are meant to be -2.0 m/s instead of 2.0 m/s, then the closest correct answer to -2.5 m/s would be B) 1.0 m/s to the left. But since the correct answer is not indicated in the choices, it is important to clarify the discrepancy or check the problem statement for accuracy.