To find the mass of the second object, we can use the conservation of momentum principle. The total momentum before the collision is equal to the total momentum after the collision.
Given:
- Mass of the first object (m₁) = 1.5 kg
- Final velocity of both objects after collision (v) = 50 m/s
- Total momentum of the system (P) = 250 kg⋅m/s
The momentum after the collision can be expressed as: \[ P = (m_1 + m_2) \cdot v \]
Where \(m_2\) is the mass of the second object. We can rearrange this to solve for \(m_2\): \[ m_1 + m_2 = \frac{P}{v} \]
Substituting the known values: \[ m_1 + m_2 = \frac{250 , \text{kg⋅m/s}}{50 , \text{m/s}} = 5 , \text{kg} \]
Now we can solve for \(m_2\): \[ 1.5 , \text{kg} + m_2 = 5 , \text{kg} \] \[ m_2 = 5 , \text{kg} - 1.5 , \text{kg} = 3.5 , \text{kg} \]
Thus, the mass of the second object is 3.5 kg.
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