Final answer:
The final velocities of the balls after the elastic collision cannot be determined without additional information or equations.
Step-by-step explanation:
The final velocities of the balls after the collision can be calculated using the principle of conservation of momentum. Momentum is conserved in an elastic collision, which means the total momentum before the collision is equal to the total momentum after the collision.
Let's calculate the total momentum before the collision:
Momentum of Izzie's ball = mass * velocity = 2.0 kg * 3.0 m/s = 6.0 kg m/s
Momentum of Marie's ball = mass * velocity = 4.0 kg * (-5.0 m/s) = -20.0 kg m/s
The total momentum before the collision is 6.0 kg m/s + (-20.0 kg m/s) = -14.0 kg m/s
Since the collision is elastic, the total momentum after the collision will also be -14.0 kg m/s.
Let's assume the velocities of Izzie's ball and Marie's ball after the collision are v1 and v2, respectively.
Applying the conservation of momentum:
2.0 kg * v1 + 4.0 kg * v2 = -14.0 kg m/s
Simplifying the equation, we get:
2v1 + 4v2 = -14
Now, we can solve this equation to find the values of v1 and v2. To solve this, we need additional information or equations such as the relationship between the velocities after the collision.
Without that additional information, it is not possible to determine the exact velocities of the balls after the collision. Additional information or equations are required to solve this problem.