To find the total momentum of the system after the collision, we first calculate the momentum of each object before the collision and then sum those values.
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Calculate the momentum of the first object (m1 = 10 kg, v1 = 5.4 m/s): \[ p_1 = m_1 \times v_1 = 10 , \text{kg} \times 5.4 , \text{m/s} = 54 , \text{kg-m/s} \]
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Calculate the momentum of the second object (m2 = 12 kg, v2 = -3.5 m/s, direction opposite to m1): \[ p_2 = m_2 \times v_2 = 12 , \text{kg} \times (-3.5 , \text{m/s}) = -42 , \text{kg-m/s} \]
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Combine the momenta to find the total momentum before the collision: \[ p_{\text{total}} = p_1 + p_2 = 54 , \text{kg-m/s} + (-42 , \text{kg-m/s}) = 54 - 42 = 12 , \text{kg-m/s} \]
Since momentum is conserved in a closed system, the total momentum after the collision will be the same as before the collision, which is 12 kg-m/s.
The total momentum of the system after the collision is 12 kg-m/s. Therefore, the answer is 12 kg-m/s (though, this option does not appear among the provided choices).