in a collision, a 25.0 kg mass moving at 3.0 m/s transfers all of its momentum to a 5.0 kg mass. what is the velocity of the 5.0 kg mass after the collision

To find the velocity of the 5.0 kg mass after the collision, we can use the principle of **conservation of momentum**. This principle states that the total momentum before the collision is equal to the total momentum after the collision, assuming no external forces are acting on the system.

### Given:
- Mass of the first object (m₁) = 25.0 kg
- Velocity of the first object (v₁) = 3.0 m/s
- Mass of the second object (m₂) = 5.0 kg
- Initial velocity of the second object (v₂) = 0 m/s (since it's not mentioned, we assume it is stationary)
- After the collision, the momentum is fully transferred to the second mass.

### Step-by-step Solution:

1. **Momentum before the collision**:  
   The momentum of the 25.0 kg mass before the collision is given by:
   \[
   p_{\text{before}} = m₁ \cdot v₁ = 25.0 \, \text{kg} \cdot 3.0 \, \text{m/s} = 75.0 \, \text{kg} \cdot \text{m/s}
   \]
   
2. **Momentum after the collision**:  
   After the collision, all of the momentum is transferred to the second object, so the momentum of the 5.0 kg mass must be equal to the initial momentum of the first mass:
   \[
   p_{\text{after}} = m₂ \cdot v₂'
   \]
   where \(v₂'\) is the velocity of the second object after the collision.

3. **Apply conservation of momentum**:
   \[
   p_{\text{before}} = p_{\text{after}}
   \]
   \[
   75.0 \, \text{kg} \cdot \text{m/s} = 5.0 \, \text{kg} \cdot v₂'
   \]

4. **Solve for \(v₂'\)**:
   \[
   v₂' = \frac{75.0 \, \text{kg} \cdot \text{m/s}}{5.0 \, \text{kg}} = 15.0 \, \text{m/s}
   \]

### Final Answer:
The velocity of the 5.0 kg mass after the collision is \(15.0 \, \text{m/s}\).

Would you like more details or further explanation?

### Related Questions:
1. What is the kinetic energy of each mass before and after the collision?
2. How would the outcome change if the second mass was moving initially?
3. How do we calculate the force exerted during the collision if the collision time is given?
4. What happens to the velocities if the masses bounce off instead of fully transferring momentum?
5. How does conservation of momentum work in an elastic collision?

### Tip:
When solving problems involving momentum, always check whether external forces are present, as they can affect the momentum conservation principle.

In a collision, a 25.0 kg mass moving at 3.0 m/s transfers all of its momentum to a 5.0 kg mass. What is the velocity of the 5.0 kg mass after the collision?

This problem demonstrates how to use the conservation of momentum to find the velocity of a 5.0 kg mass after a 25.0 kg mass transfers all of its momentum during a collision. Detailed steps and formulas are provided for Grades 9-11 students.

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