To determine the velocity at which the crashed cars move after the collision, 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, provided no external forces are acting on the system.
The momentum of an object is defined as the product of its mass and velocity. So, let's calculate the momentum of each car before the collision:
Momentum of the first car (m1) = mass (m1) × velocity (v1) = 1000 kg × (80 km/h) = 1000 kg × (80,000 m/3600 s) ≈ 22222.22 kg·m/s
Momentum of the second car (m2) = mass (m2) × velocity (v2) = 1000 kg × (60 km/h) = 1000 kg × (60,000 m/3600 s) ≈ 16666.67 kg·m/s
The total momentum before the collision is the sum of the individual momenta of the two cars:
Total initial momentum = Momentum of the first car + Momentum of the second car = 22222.22 kg·m/s + 16666.67 kg·m/s = 38888.89 kg·m/s
After the collision, the cars get stuck together, which means they move with a common final velocity (v_final). The combined mass of the two cars is:
Total mass (M_total) = mass of the first car (m1) + mass of the second car (m2) = 1000 kg + 1000 kg = 2000 kg
Using the conservation of momentum, the total final momentum is equal to the total initial momentum:
Total final momentum = Total initial momentum M_total × v_final = 38888.89 kg·m/s
Now, we can solve for v_final:
v_final = 38888.89 kg·m/s ÷ 2000 kg ≈ 19.44 m/s
Therefore, the crashed cars move together at a velocity of approximately 19.44 meters per second after the collision.