A railroad diesel engine weighs 3.6 times as much as a freightcar. If the diesel engine coasts at 4.3 km/h into a freightcar that is initially at rest, how fast do the two coast after they couple together? )

Apply the law of conservation of momentum. Show your work if you have further questions.

To find out how fast the diesel engine and the freight car will coast after they couple together, we need to use the principle of conservation of momentum.

The principle of conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it. In this case, the diesel engine and the freight car can be considered as an isolated system since no external forces are acting on them.

Let's denote the weight of the freight car as W. According to the problem, the weight of the diesel engine is 3.6 times the weight of the freight car, so the weight of the diesel engine is 3.6W.

When the diesel engine coasts into the stationary freight car, the initial momentum of the system is zero since neither of them is moving initially. Let's assume the final speed of the coupled system is v.

The momentum of the diesel engine before the coupling is given by the equation:
Momentum = Mass x Velocity
Momentum of diesel engine = (3.6W) x (4.3 km/h)

Likewise, the momentum of the freight car before the coupling is given by:
Momentum of freight car = W x 0 km/h (since it is initially at rest)

According to the principle of conservation of momentum, the total momentum before the coupling must equal the total momentum after the coupling:

Momentum before = Momentum after
(3.6W) x (4.3 km/h) + W x 0 km/h = (3.6W + W) x v

Simplifying the equation:
(3.6W) x (4.3 km/h) = (4.6W) x v

Now we can solve for v, the final speed of the coupled system:
v = (3.6W) x (4.3 km/h) / (4.6W)

Cancelling out the weight term:
v = (3.6 x 4.3) km/h

Evaluating the expression:
v = 15.48 km/h

Therefore, the diesel engine and the freight car will coast together at a speed of approximately 15.48 km/h after they couple together.