Final answer:
The velocity of the 2540 kg car before the collision was approximately 15.55 m/s to the north. This was determined using conservation of linear momentum and the known velocities and masses of the cars involved in the collision.
Step-by-step explanation:
To find the velocity of the 2540 kg car before the collision, we use the principle of conservation of momentum. The total momentum of a system remains constant if no external forces act upon it. In this case, we assume that the collision is perfectly inelastic because the two cars stick together after the collision.
The formula for the conservation of linear momentum is:
m1 * v1 + m2 * v2 = (m1 + m2) * v',
where m1 and m2 are the masses of the cars, v1 and v2 are the velocities of the cars before collision, and v' is the velocity of the combined mass after collision.
Let's designate the 1500 kg car moving south (negative direction) as car 1, and the 2540 kg car moving north as car 2. The final velocity (v') is given as 5.07 m/s to the north (positive direction).
Substitute the known values into the momentum conservation equation to solve for v2:
1500 kg * (-12.6 m/s) + 2540 kg * v2 = (1500 kg + 2540 kg) * 5.07 m/s
Solving for v2:
2540 kg * v2 = (4040 kg * 5.07 m/s) - (1500 kg * (-12.6 m/s))
2540 kg * v2 = 20482.8 kg*m/s + 18900 kg*m/s
v2 = (20482.8 kg*m/s + 18900 kg*m/s) / 2540 kg
v2 = 15.55 m/s
Therefore, the velocity of the 2540 kg car before the collision was approximately 15.55 m/s to the north.