Boxcar A, with a mass of 1500 kg, is travelling at 25 m/s to the east. Boxcar B has a mass of 2000 kg, and is initially at rest. The boxcars collide inelastically and move together after they get stuck. What is their combined velocity?

To solve this problem, we can apply 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 in an isolated system.

The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) can be calculated using the formula:

p = m * v

Where:
p = momentum
m = mass
v = velocity

Before the collision:

Momentum of boxcar A = mass of boxcar A * velocity of boxcar A
Momentum of boxcar B = mass of boxcar B * velocity of boxcar B

After the collision:

Combined momentum = total mass of boxcar A and boxcar B * combined velocity

Since the boxcars stick together and move as one after the collision, they share the same velocity.

Using the principle of conservation of momentum, we can equate the total momentum before the collision to the combined momentum after the collision:

Momentum of boxcar A + Momentum of boxcar B = Combined momentum

Setting up the equation:

(mass of boxcar A * velocity of boxcar A) + (mass of boxcar B * velocity of boxcar B) = (total mass of boxcar A and boxcar B) * combined velocity

Plugging in the given values:

(1500 kg * 25 m/s) + (2000 kg * 0 m/s) = (1500 kg + 2000 kg) * combined velocity

Simplifying the equation:

37500 kg * m/s = 3500 kg * combined velocity

Dividing both sides of the equation by 3500 kg:

combined velocity = 37500 kg * m/s / 3500 kg

Simplifying:

combined velocity ≈ 10.71 m/s

So, the combined velocity of the boxcars after collision is approximately 10.71 m/s.