A railway wagon of mass 15 t is moving along a level track at 10 km/h when it collides and couples together with a second wagon of mass 30 t moving in the same direction at 5 km/h. if the two wagons couple together after the impact, what would be their common velocity?

just conserve momentum before and after the collision. You then have

15*10 + 30*5 = (15+30)v

But don't you convert it into the base units?

To find the common velocity of the two coupled wagons after the impact, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

The momentum of an object is determined by its mass and velocity. The formula for momentum is:

Momentum = mass × velocity

First, let's convert the speeds from kilometers per hour (km/h) to meters per second (m/s) to ensure consistent units:

10 km/h = (10/3.6) m/s = 100/36 m/s
5 km/h = (5/3.6) m/s = 5/18 m/s

Now, we can calculate the momentum of each wagon before the collision:

Momentum of the first wagon = mass × velocity
= 15,000 kg × (100/36) m/s
= 41,667 kg·m/s

Momentum of the second wagon = mass × velocity
= 30,000 kg × (5/18) m/s
= 8,333 kg·m/s

Considering that the total momentum before the collision is equal to the total momentum after the collision, we can set up an equation:

Total momentum before = Total momentum after

(41,667 kg·m/s) + (8,333 kg·m/s) = Total momentum after

Now, we have the sum of the individual momenta of the wagons before the collision, and we need to find the common velocity (v) of the two coupled wagons after the impact.

To solve for v, we can rearrange the equation:

Total momentum after = (mass of the coupled wagons) × v

Substituting the given masses:

(15,000 kg + 30,000 kg) × v = 41,667 kg·m/s + 8,333 kg·m/s

45,000 kg × v = 50,000 kg·m/s

Dividing both sides by 45,000 kg:

v = 50,000 kg·m/s / 45,000 kg

v ≈ 1.11 m/s

Therefore, the common velocity of the two coupled wagons after the impact is approximately 1.11 m/s.