Final answer:
The final velocity of the 10kg ball after the collision is approximately -3.98 m/s.
Step-by-step explanation:
To solve this problem, we can use the law of conservation of momentum, which states that the total momentum before a collision is equal to the total momentum after a collision in an isolated system.
Let's calculate the momentum of each ball before the collision:
- The momentum of the 12kg ball before the collision is given by its mass (12kg) multiplied by its velocity (2.5m/s), which is 30 kg·m/s.
- The momentum of the 10kg ball before the collision is given by its mass (10kg) multiplied by its velocity (-3.5m/s), which is -35 kg·m/s.
After the collision, the 12kg ball is traveling at -2.9m/s. Let's calculate its momentum:
- The momentum of the 12kg ball after the collision is given by its mass (12kg) multiplied by its velocity (-2.9m/s), which is -34.8 kg·m/s.
Now, we can use the law of conservation of momentum to calculate the final velocity of the 10kg ball:
Total momentum before collision = Total momentum after collision
30 kg·m/s + (-35 kg·m/s) = -34.8 kg·m/s + (10kg * final velocity of the 10kg ball)
Simplifying the equation:
-5 kg·m/s - 34.8 kg·m/s = 10kg * final velocity of the 10kg ball
-39.8 kg·m/s = 10kg * final velocity of the 10kg ball
Dividing both sides of the equation by 10kg:
final velocity of the 10kg ball = -3.98 m/s
Therefore, the final velocity of the 10kg ball after the collision is approximately -3.98 m/s.