Two equal mass cars collide head to tail and their bumpers lock. One car has a velocity of 10 m/s and the other is at rest. What is the velocity of the two cars after the collision?
To find the velocity of the two cars after the collision, we can apply the law of conservation of momentum. According to this law, the total momentum before the collision should be equal to the total momentum after the collision.
1. Let's define the variables:
- m: mass of each car (same for both cars)
- v1: initial velocity of the first car (10 m/s)
- v2: initial velocity of the second car (0 m/s)
- V: final velocity of both cars after the collision
2. Apply the law of conservation of momentum:
- Total momentum before collision = Total momentum after collision
- (m * v1) + (m * v2) = (2m * V) (since the total mass after the collision is twice the mass of each car)
3. Plug in the values:
- (m * 10) + (m * 0) = (2m * V)
- 10m = 2mV
4. Simplify the equation:
- Divide both sides of the equation by 2m:
- 10 = 2V
5. Solve for V:
- Divide both sides of the equation by 2:
- V = 5
Therefore, the velocity of both cars after the collision is 5 m/s.