Answer :
Using the principle of conservation of momentum, we find that the combined train cars have a final velocity of approximately 13.96 m/s after the collision. This calculation demonstrates how momentum is conserved in collisions, with the final velocity determined by the masses and initial velocities of the colliding objects.
To find the final velocity of the two train cars after the collision, we can use the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.
Let [tex]\( v_f \)[/tex] be the final velocity of the combined train cars. Using the conservation of momentum equation:
[tex]\[ (m_1 \times v_{1i}) + (m_2 \times v_{2i}) = (m_1 + m_2) \times v_f \]Where:\( m_1 = 235 \) kg (mass of first train car)\( v_{1i} = 32 \) m/s (initial velocity of first train car)\( m_2 = 137 \) kg (mass of second train car)\( v_{2i} = -17 \) m/s (initial velocity of second train car)Substituting the given values:\[ (235 \times 32) + (137 \times -17) = (235 + 137) \times v_f \]\[ (7520) - (2329) = (372) \times v_f \]\[ 5191 = 372 \times v_f \]\[ v_f = \frac{5191}{372} \]\[ v_f = 1[/tex]
So, the final velocity of the combined train cars after the collision is approximately 13.96 m/s.
