Final answer:
The common velocity of the two-car train after a collision in which one car is initially at rest can be determined using the conservation of linear momentum. Without complete mass values in the question, we cannot proceed with a calculation, but assuming masses of 1.00 × 104 kg and 2.00 × 104 kg, the combined velocity would be 8.33 m/s eastward.
Step-by-step explanation:
To find the common velocity py of the two-car train after the collision, we use the principle of the conservation of linear momentum. This principle states that if no external forces are acting on a system, the total momentum of the system remains constant. In this case, the system is our two train cars before and after the collision.
The total initial momentum of the system is the sum of the momentum of each car before the collision. Since one car is at rest, its initial momentum is zero. Therefore, the initial momentum of the system is:
(1.00 × 10kg × 25.0 m/s) + (2.00 × 10kg × 0 m/s).
The total final momentum of the system is the combined mass of the two cars multiplied by their common velocity after the collision:
(1.00 × 10kg + 2.00 × 10kg) × py.
Setting the total initial momentum equal to the total final momentum and solving for py gives us the common velocity. Unfortunately, the question does not provide complete values for the masses, so the calculation cannot be completed without the actual mass values. Assuming the mass values were meant to be 1.00 × 104 kg for the first car and 2.00 × 104 kg for the second car, the equation can be calculated as follows:
(1.00 × 104 kg × 25.0 m/s) = (1.00 × 104 kg + 2.00 × 104 kg) × py
py = × 25.0 m/s / 3.00 × 104 kg
py = 8.33 m/s
Therefore, the common velocity of the two-car train after the collision is 8.33 m/s due east.