This problem can be solved using the principle of conservation of momentum. Since the two balls stick together after the collision, it's a perfectly inelastic collision. In such cases, the total momentum before the collision is equal to the total momentum after the collision.

Step 1: Write the formula for the conservation of momentum:

$m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f$ where:

• $m_1 = 2 \, \text{kg}$ (mass of the first ball),
• $v_1 = 1.5 \, \text{m/s}$ (velocity of the first ball),
• $m_2 = 3 \, \text{kg}$ (mass of the second ball),
• $v_2 = -2.0 \, \text{m/s}$ (velocity of the second ball; negative since it's travelling in the opposite direction),
• $v_f$ is the final velocity of the two balls after the collision.

Step 2: Substitute the values into the equation:

$(2 \times 1.5) + (3 \times -2.0) = (2 + 3) v_f$ $3 - 6 = 5 v_f$ $-3 = 5 v_f$

Step 3: Solve for $v_f$:

$v_f = \frac{-3}{5} = -0.6 \, \text{m/s}$

Conclusion:

The velocity of the two balls after the collision is 0.6 m/s to the left (since the negative sign indicates the direction is to the left).

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Would you like more details on the concept of momentum or clarification on the steps? Here are some related questions you can try:

1. What happens to kinetic energy in a perfectly inelastic collision?
2. How would the result differ if the balls didn’t stick together?
3. Can momentum be conserved in an inelastic collision if external forces act on the system?
4. How would the final velocity change if both balls had the same mass?
5. What would be the final velocity if both balls were initially at rest?

Tip: In inelastic collisions, momentum is always conserved, but kinetic energy is not.