Ryan driving a 2.0 x 10^3 kg car traveling 15 m/s "rear ends" the car Emma is driving with a mass of 1.0 x 10^3 kg. Emma's car was initially moving 6.0 m/s in the same direction as Ryan's car. What is the common velocity of the two cars after the collision if they lock together during impact?
To solve this problem, we can use the principle of conservation of momentum. The total momentum before the collision is equal to the total momentum after the collision.
The total momentum before the collision can be calculated as:
Initial momentum of Ryan's car = 2.0 x 10^3 kg * 15 m/s = 3.0 x 10^4 kg*m/s
Initial momentum of Emma's car = 1.0 x 10^3 kg * 6.0 m/s = 6.0 x 10^3 kg*m/s
Total initial momentum = 3.0 x 10^4 kg*m/s + 6.0 x 10^3 kg*m/s = 3.6 x 10^4 kg*m/s
After the collision, the two cars lock together and move with a common velocity. Let's call this common velocity v. The total momentum after the collision is given by the mass of the combined cars (2.0 x 10^3 kg + 1.0 x 10^3 kg = 3.0 x 10^3 kg) multiplied by the common velocity v:
Total final momentum = 3.0 x 10^3 kg * v
According to the principle of conservation of momentum, the total initial momentum is equal to the total final momentum:
3.6 x 10^4 kg*m/s = 3.0 x 10^3 kg * v
v = (3.6 x 10^4 kg*m/s) / (3.0 x 10^3 kg) = 12 m/s
Therefore, the common velocity of the two cars after the collision is 12 m/s.