Final answer:
Using conservation of momentum, we can determine that after the collision, ball B has a velocity of -1.65 m/s westward.
Step-by-step explanation:
To find the velocity of ball B after the collision, we can use the principle of conservation of momentum. As long as the forces between the balls are internal, the momentum of the system consisting of both balls is conserved. For a collision in one dimension:
Total momentum before collision = Total momentum after collision
The momentum of ball A before the collision is its mass times its velocity, and likewise for ball B. Similarly, we calculate the momentum of these balls after the collision. Here's how the equation for conservation of momentum looks for our situation:
(Mass of ball A × Velocity of ball A before collision) + (Mass of ball B × Velocity of ball B before collision) = (Mass of ball A × Velocity of ball A after collision) + (Mass of ball B × Velocity of ball B after collision)
Given that ball A's mass is 6 kg and its velocity before collision is 3.5 m/s westward (which we'll take as negative for calculation) and after collision is 1.6 m/s westward (also negative), and ball B's mass is 4 kg with a velocity of 1.2 m/s eastward (positive for calculation), we substitute these values into the equation.
(6 kg × -3.5 m/s) + (4 kg × 1.2 m/s) = (6 kg × -1.6 m/s) + (4 kg × Velocity of ball B after collision)
Solving for the velocity of ball B after collision:
(-21 kg·m/s) + (4.8 kg·m/s) = (-9.6 kg·m/s) + (4 kg × Velocity of ball B after collision)
(-16.2 kg·m/s) = (-9.6 kg·m/s) + (4 kg × Velocity of ball B after collision)
Velocity of ball B after collision = ((-16.2 kg·m/s) + (9.6 kg·m/s)) / 4 kg
Velocity of ball B after collision = (-6.6 kg·m/s) / 4 kg = -1.65 m/s (westward)
So, after the collision, ball B has a velocity of -1.65 m/s westward.