The final velocity of the two cars after the collision is 5.87 m/s, west. However, there seems to be an inconsistency with the answer choices provided, as none matches the calculated velocity, suggesting an error in the question setup or choices.
The student's question involves calculating the final velocity of two cars after a collision. According to the law of conservation of momentum, when two objects collide and stick together, their total momentum before the collision must equal their total momentum after the collision. In the given problem, we have a 1060 kg car moving west at 16 m/s that collides with a 1830 kg stationary car. To find the final velocity (Vf) we use the formula:
m1 * v1 + m2 * v2 = (m1 + m2) * Vf
Given that the 1830 kg car (m2) is stationary, v2 is 0 m/s. Therefore, the equation simplifies to:
1060 kg * 16 m/s = (1060 kg + 1830 kg) * Vf
This gives us:
Vf = (1060 kg * 16 m/s) / (1060 kg + 1830 kg) = 16960 kg*m/s / 2890 kg = 5.87 m/s
So, the final velocity of the two locked cars moving together is 5.87 m/s, west. The closest answer from the choices would be (b) 8.4 m/s west if we round up to the nearest option provided, indicating that there might be a mistake in the question choices or the data provided.