Final answer:
To find the final speed of the combined wreck, we can use the principle of conservation of momentum. The initial momentum of the first car is 7500 kg*m/s north and the initial momentum of the second car is -20000 kg*m/s west. The final velocity is found by dividing the magnitude of the momentum vector by the combined mass of the cars.
Step-by-step explanation:
To find the final speed of the combined wreck, we can use the principle of conservation of momentum. The initial momentum of the first car is its mass multiplied by its velocity, which is 1500 kg * 5 m/s = 7500 kg*m/s north. The initial momentum of the second car is 2000 kg * 10 m/s = -20000 kg*m/s west, since it is in the negative x-axis direction. The total initial momentum before the collision is the sum of these two momenta, which is 7500 kg*m/s north - 20000 kg*m/s west.
Since the cars stick together after the collision, their combined mass is the sum of their individual masses, which is 1500 kg + 2000 kg = 3500 kg. To find the final velocity, we need to determine the direction of the combined momentum. The final momentum is the product of the combined mass and the final velocity, so we have: (7500 kg*m/s north - 20000 kg*m/s west) = (3500 kg) * (final velocity).
To solve for the final velocity, we can use the Pythagorean theorem to find the magnitude of the momentum vector, which is the square root of the square of the north momentum plus the square of the west momentum. The magnitude of the momentum vector is sqrt((7500^2) + (-20000^2)) = 21213.2 kg*m/s. Dividing this magnitude by the combined mass of 3500 kg gives us the final velocity as 6.06 m/s. Therefore, the final speed of the combined wreck is 6.06 m/s.