Final answer:
The velocity of the train cars after the collision is 0.75 m/s to the east, obtained by applying the conservation of momentum principle and solving for the final velocity. None of the provided options match the calculated result.
Step-by-step explanation:
The scenario involves two train carts with different masses moving in opposite directions. To find the velocity of the carts after the collision, we use the principle of conservation of momentum. Momentum before collision equals momentum after collision when no external forces are acting.
The formula for momentum is p = mv, where p is momentum, m is mass, and v is velocity. The first cart's momentum is (500 kg)(12 m/s) = 6000 kg·m/s to the east, and the second cart's momentum is (300 kg)(18 m/s) = 5400 kg·m/s to the west. Because they move in opposite directions, we consider the momentum of the second cart as negative. Thus, combined momentum before collision is 6000 kg·m/s - 5400 kg·m/s = 600 kg·m/s to the east.
After collision, the two carts stick together, so their combined mass is 500 kg + 300 kg = 800 kg. The total momentum must be conserved, so the velocity v after collision can be found using the equation p = mv:
600 kg·m/s = (800 kg)(v)
Solving for v, we get:
v = 600 kg·m/s / 800 kg = 0.75 m/s to the east.
The final velocity of the train cars after the collision is 0.75 m/s to the east, which is not listed in the options given.