To find the mass of the second object, we can use the principle of conservation of momentum. The total momentum before the collision should equal the total momentum after the collision.
Let's denote:
- \( m_1 \) = mass of the first object = 1.5 kg
- \( m_2 \) = mass of the second object
- \( v \) = final velocity of both objects after the collision = 50 m/s
- Total momentum \( p \) = 250 kg·m/s
The total momentum after the collision can be expressed as: \[ p = (m_1 + m_2) v \]
Substituting the values we know: \[ 250 , \text{kg·m/s} = (1.5 , \text{kg} + m_2)(50 , \text{m/s}) \]
Now, we can solve for \( m_2 \).
First, divide both sides by 50 m/s: \[ \frac{250 , \text{kg·m/s}}{50 , \text{m/s}} = 1.5 , \text{kg} + m_2 \] \[ 5 , \text{kg} = 1.5 , \text{kg} + m_2 \]
Now, subtract 1.5 kg from both sides to isolate \( m_2 \): \[ m_2 = 5 , \text{kg} - 1.5 , \text{kg} \] \[ m_2 = 3.5 , \text{kg} \]
Thus, the mass of the second object is 3.5 kg.
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