Understanding the Concepts

* Perfectly Inelastic Collision: In a perfectly inelastic collision, the objects stick together after the collision, moving as a single unit.

* Conservation of Momentum: The total momentum of a system before a collision is equal to the total momentum after the collision.

Setting Up the Problem

* Let:

* m_a = mass of ball A

* m_b = mass of ball B

* v_a = initial velocity of ball A (5 m/s)

* v_b = initial velocity of ball B (-2 m/s - negative since it's moving towards A)

* v_f = final velocity of the combined mass

Applying Conservation of Momentum

1. Initial Momentum: The total momentum before the collision is:

m_av_a + m_bv_b

2. Final Momentum: The total momentum after the collision (when they move together) is:

(m_a + m_b)v_f

3. Conservation: The initial momentum equals the final momentum:

m_av_a + m_bv_b = (m_a + m_b)v_f

Solving for the Final Velocity (v_f)

To find v_f, we need to rearrange the equation:

v_f = (m_av_a + m_bv_b) / (m_a + m_b)

Important Note: Without knowing the masses of the balls (m_a and m_b), we cannot calculate a numerical value for the final velocity.

Example:

Let's assume:

* m_a = 1 kg

* m_b = 2 kg

Then, the final velocity would be:

v_f = (1 kg * 5 m/s + 2 kg * -2 m/s) / (1 kg + 2 kg) = 1/3 m/s

Therefore, the velocity of the combined mass after the collision depends on the masses of the balls. The equation above will give you the final velocity once you know the masses.