A boxcar of mass 3.21 x 10^4 kg is rolling south at 5.16 m/s when it collides and couples with another boxcar of mass 5.18 x 10^4 kg that is rolling north at 2.38 m/s. What is the velocity of the coupled boxcars after collision? Take north as positive and express your result to three significant digits.

Please help!

conservation of momentum

3.21E4(-5.16)+5.18E4(2.38)=(summasses) V
solve for V

-.505

To solve this problem, we can apply the law of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces act on it.

The momentum (p) of an object can be calculated by multiplying its mass (m) by its velocity (v): p = m * v.

Before the collision, we have two boxcars with their respective masses and velocities:

Mass of boxcar 1 (m1) = 3.21 x 10^4 kg
Velocity of boxcar 1 (v1) = 5.16 m/s (south, negative direction)

Mass of boxcar 2 (m2) = 5.18 x 10^4 kg
Velocity of boxcar 2 (v2) = 2.38 m/s (north, positive direction)

To solve for the velocity of the coupled boxcars after the collision, we need to find the total momentum before and after the collision and equate them.

The total momentum before the collision (p_total_initial) is given by the sum of the momenta of both boxcars.

p_total_initial = p1_initial + p2_initial
= (m1 * v1) + (m2 * v2)

Let's substitute the given values:

p_total_initial = (3.21 x 10^4 kg * -5.16 m/s) + (5.18 x 10^4 kg * 2.38 m/s)

Evaluating this expression will give us the total momentum before the collision.

Next, we can use the principle of conservation of momentum to find the velocity of the coupled boxcars after the collision.

The total momentum after the collision (p_total_final) will be the same as the total momentum before the collision. Since the two boxcars couple and move together as one unit, their masses can be combined:

p_total_final = (m1 + m2) * v_final

Let's rearrange the equation and solve for v_final:

v_final = p_total_final / (m1 + m2)

Substitute the known values into the equation to find the velocity of the coupled boxcars after the collision.

Evaluate the expression to get the solution expressed to three significant digits.