Suppose a clay model of a koala bear has a mass of 0.240 kg and slides on ice at a speed of 0.735 m/s. It runs into another clay model, which is initially motionless and has a mass of 0.335 kg. Both being soft clay, they naturally stick together. What is their final velocity (in m/s)?

To solve this problem, we can use the principle of **conservation of momentum**. When two objects collide and stick together, their combined momentum after the collision is equal to the total momentum before the collision. This is because momentum is conserved in collisions when there are no external forces.

### Given Data:
- Mass of the first clay model (\( m_1 \)) = 0.240 kg
- Initial velocity of the first clay model (\( v_1 \)) = 0.735 m/s
- Mass of the second clay model (\( m_2 \)) = 0.335 kg
- Initial velocity of the second clay model (\( v_2 \)) = 0 m/s (since it is initially motionless)

### Conservation of Momentum:
The total momentum before the collision is equal to the total momentum after the collision:
\[
m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_f
\]
where \( v_f \) is the final velocity of the combined clay models after they stick together.

### Calculation:

1. **Calculate the total initial momentum**:
   \[
   \text{Initial Momentum} = (0.240 \, \text{kg}) \times (0.735 \, \text{m/s}) + (0.335 \, \text{kg}) \times (0 \, \text{m/s})
   \]
   \[
   \text{Initial Momentum} = 0.240 \times 0.735 = 0.1764 \, \text{kg m/s}
   \]

2. **Calculate the final velocity**:
   \[
   v_f = \frac{\text{Total Initial Momentum}}{m_1 + m_2} = \frac{0.1764 \, \text{kg m/s}}{0.240 \, \text{kg} + 0.335 \, \text{kg}}
   \]
   \[
   v_f = \frac{0.1764}{0.575} \approx 0.307 \, \text{m/s}
   \]

### Answer:
The final velocity of the combined clay models is approximately:
\[
v_f \approx 0.307 \, \text{m/s}
\]

Would you like further clarification on any part of this solution?

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Here are 5 related questions to expand your understanding:

1. What would happen if the second clay model also had an initial velocity in the opposite direction?
2. How would the final velocity change if both objects had the same initial speed?
3. What principle allows us to use conservation of momentum in this scenario?
4. How would the outcome differ if the objects did not stick together after the collision?
5. Can you explain how kinetic energy changes in this inelastic collision?

**Tip:** Conservation of momentum is always valid in isolated systems, but kinetic energy is only conserved in perfectly elastic collisions.

Suppose a clay model of a koala bear has a mass of 0.240 kg and slides on ice at a speed of 0.735 m/s. It runs into another clay model, which is initially motionless and has a mass of 0.335 kg. Both being soft clay, they naturally stick together. What is their final velocity (in m/s)?

Find out how to calculate the final velocity of two clay models that collide and stick together. This problem involves using the conservation of momentum principle, given the mass and initial speed of each model. Suitable for high school physics students in Grades 10-12.

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