Question

Consider a run away train. The train has a mass of 200,000 kg. The train is traveling at 25 m/s . In an attempt to slow down the the train, the engineer puts another train in the run away train's path. The second train has a mass of 150,000kg. The second train is traveling at 15m/s in the same direction as the run away train. When the trains collide, they stick together. How fast will the train be traveling after the collision ( assume the train are not being powered by engines)

Answer 1

$$\begin{array}{l} m1 = 200000kg \\ m2 = 150000kg \\ v1 = 25 \frac{m}{s} \\ v2 = 15 \frac{m}{s} \\ \end{array}$$

Before collision:

$$\begin{array}{l} p1 = m1v1 \\ p2 = m2v2 \\ \end{array}$$

After collision:

$$p = (m1 + m2)v$$

The law of conservation of momentum:

$$\begin{array}{l} p1 + p2 = p \\ m1v1 + m2v2 = (m1 + m2)v \\ \end{array}$$

The velocity after collision is:

$$v = \frac{m1v1 + m2v2}{m1 + m2} = \frac{200000 * 25 + 150000 * 15}{200000 + 150000} = \frac{7250000}{350000} = 20.7 \frac{m}{s}$$