To find the mass of the second object, we can use the principle of conservation of momentum. The total momentum before the collision equals the total momentum after the collision.
Given:
- Mass of the first object, \( m_1 = 1.5 , \text{kg} \)
- Final velocity of the combined objects, \( v_f = 50 , \text{m/s} \)
- Total momentum of the system, \( p_{\text{total}} = 250 , \text{kg} \cdot \text{m/s} \)
The momentum of the system after the collision can be expressed as: \[ p_{\text{total}} = (m_1 + m_2) v_f \] where \( m_2 \) is the mass of the second object.
Substituting the known values into the equation: \[ 250 = (1.5 + m_2) \cdot 50 \]
Now, let's simplify and solve for \( m_2 \): \[ 250 = 50 \cdot (1.5 + m_2) \]
Dividing both sides by 50: \[ 5 = 1.5 + m_2 \]
Subtracting 1.5 from both sides: \[ m_2 = 5 - 1.5 \] \[ m_2 = 3.5 , \text{kg} \]
Thus, the mass of the second object is 3.5 kg.