Physics – 1.6 Momentum | e-Consult

Solution:

We use the conservation of momentum. The total momentum before the collision equals the total momentum after the collision.

Initial momentum (p_i) = m_A * v_A + m_B * v_B = (3.0 kg * 4.0 m/s) + (1.0 kg * -2.0 m/s) = 12.0 kg m/s - 2.0 kg m/s = 10.0 kg m/s (to the right)

Final momentum (p_f) = (m_A + m_B) * v_f = (3.0 kg + 1.0 kg) * v_f = 4.0 kg * v_f

Since momentum is conserved, p_i = p_f. Therefore:

10.0 kg m/s = 4.0 kg * v_f

v_f = 10.0 kg m/s / 4.0 kg = 2.5 m/s (to the right)

Therefore, the velocity of the combined carts immediately after the collision is 2.5 m/s to the right.