Final answer:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. The velocity of the rail flatcar immediately after the collision, if they fail to connect, will be approximately 1.63 m/s.
Step-by-step explanation:
According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision.
Step 1: Calculate the momentum of the rail flatcar before the collision.
The momentum of an object is calculated by multiplying its mass and velocity.
Momentum of the rail flatcar before collision = mass of rail flatcar × velocity of rail flatcar
Momentum of the rail flatcar before collision = 9402 kg × 0.65 m/s
Momentum of the rail flatcar before collision = 6111.3 kg·m/s
Step 2: Calculate the momentum of the boxcar after the collision.
The momentum of the boxcar after the collision can be calculated using the same formula as above.
Momentum of the boxcar after collision = mass of boxcar × velocity of boxcar
Momentum of the boxcar after collision = 18086 kg × 0.51 m/s
Momentum of the boxcar after collision = 9222.86 kg·m/s
Step 3: Calculate the velocity of the rail flatcar after the collision.
Since the two cars fail to connect, their final velocities will be different. The total momentum after the collision is equal to the sum of the momentum of the rail flatcar and the momentum of the boxcar after the collision.
Total momentum after collision = 6111.3 kg·m/s + 9222.86 kg·m/s = 15334.16 kg·m/s
Now we can calculate the velocity of the rail flatcar after the collision using the formula:
Velocity of the rail flatcar after collision = Total momentum after collision / mass of rail flatcar
Velocity of the rail flatcar after collision = 15334.16 kg·m/s / 9402 kg
Velocity of the rail flatcar after collision ≈ 1.63 m/s
Therefore, the velocity of the rail flatcar immediately after the collision if they fail to connect will be approximately 1.63 m/s.