To find the mass of the second object, we can use the principle of conservation of momentum.
The total momentum of a closed system before and after the collision remains the same. The momentum before the collision can be expressed as the sum of the momenta of both objects.
Given:
- Mass of the first object (m1) = 1.5 kg
- Final velocity of both objects after collision (v) = 50 m/s
- Total momentum (P) = 250 kg·m/s
First, we calculate the total momentum after the collision:
\[ P = (m_1 + m_2) \cdot v \]
Where:
- m2 = mass of the second object
- v = final velocity = 50 m/s
Setting the total momentum equal to P:
\[ 250 \text{ kg·m/s} = (1.5 \text{ kg} + m_2) \cdot 50 \text{ m/s} \]
Now, we can solve for \( m_2 \):
- Divide both sides by 50 m/s:
\[ \frac{250 \text{ kg·m/s}}{50 \text{ m/s}} = 1.5 \text{ kg} + m_2 \]
\[ 5 \text{ kg} = 1.5 \text{ kg} + m_2 \]
- Solve for \( m_2 \):
\[ m_2 = 5 \text{ kg} - 1.5 \text{ kg} \]
\[ m_2 = 3.5 \text{ kg} \]
Therefore, the mass of the second object is 3.5 kg.
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