Question

A 10,000-kg freight car moving at 2 m/s collides with a stationary 15,000-kg freight car. The two cars couple together and move off at:

a) 0.8 m/s
b) 1 m/s
c) 1.3 m/s
d) 2 m/s

Answer 1

The final velocity of the coupled cars is 0.8 m/s.

Step-by-step explanation:

In this problem, we can use the principle of conservation of momentum to determine the final velocity of the two cars. The total momentum before the collision is equal to the total momentum after the collision.

Before the collision:

• Mass of car A, mA = 10,000 kg
• Velocity of car A, vA = 2 m/s
• Mass of car B, mB = 15,000 kg
• Velocity of car B, vB = 0 m/s (stationary)

After the collision:

• Final velocity of the coupled cars, vf

Using the principle of conservation of momentum:

Total initial momentum = Total final momentum

(mA * vA) + (mB * vB) = (mA + mB) * vf

Simplifying the equation:

(10,000 kg * 2 m/s) + (15,000 kg * 0 m/s) = (10,000 kg + 15,000 kg) * vf

20,000 kg*m/s = 25,000 kg * vf

vf = 20,000 kg*m/s ÷ 25,000 kg

vf = 0.8 m/s

Therefore, the two cars move off at a final velocity of 0.8 m/s.