To find the mass of the second object, we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision.
Let \( m_1 = 1.5 , \text{kg} \) (mass of the first object) and \( m_2 \) be the mass of the second object. The velocity of both objects after the collision is given as \( v_f = 50 , \text{m/s} \).
The total momentum after the collision is given by:
\[ \text{Total Momentum} = (m_1 + m_2) \cdot v_f \]
According to the problem, the total momentum is \( 250 , \text{kg} \cdot \text{m/s} \). We can set up the equation:
\[ (m_1 + m_2) \cdot v_f = 250 \]
Substituting the values we have:
\[ (1.5 + m_2) \cdot 50 = 250 \]
Now, we can solve for \( m_2 \):
\[ 1.5 + m_2 = \frac{250}{50} \]
\[ 1.5 + m_2 = 5 \]
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.