Final answer:
The speed of the balls after a perfectly inelastic collision will be 0.67 m/s, and the direction will be to the left, as determined by the conservation of momentum.
Step-by-step explanation:
Understanding Inelastic Collisions
To find the speed and direction after a perfectly inelastic collision, we can use the principle of conservation of momentum. The initial momentum of the system can be calculated by adding the momentum of both balls.
The initial momentum of the 100 g ball (moving to the right) is
(0.1 kg) × (4 m/s) = 0.4 kg·m/s to the right. The initial momentum of the 200 g ball (moving to the left) is (0.2 kg) × (-3.0 m/s) = -0.6 kg·m/s to the right (negative because it's to the left). Adding both gives a total initial momentum of -0.2 kg·m/s.
Since the collision is perfectly inelastic, the balls stick together, and their combined mass is 0.3 kg. To find the final velocity, we use the formula:
Initial momentum = Final momentum
-0.2 kg·m/s = (0.3 kg) × (Final velocity)
Solving for the final velocity gives us -0.67 m/s, which means the combined mass moves to the left at 0.67 m/s after the collision.