Question

A 25 kg object moving with a velocity of 3.0 m/s to the right collides with a 15 kg object moving to the left at 6.0 m/s. Find the velocity of the 25 kg object after the collision, if the 15 kg object continues to move to the left but only at 0.30 m/s

Answer 1

$m_1 = 25 \; kg \\ m_2 = 15 \; kg \\ u_1 = 3i \; m/s \\ u_2 = -6i \; m/s \\ v_2 = -0.3i \; m/s$

Momentum of the system before collision is

$p_i = m_1u_1 + m_2u_2 \\ = (25 \times 3)i + (-15 \times 6)i \\ = 75i -80i \\ = -5i \; kg \; m/s$

Momentum of the system after collision is

$p_f = m_1v_1 +m_2v_2 \\ = 25v_1 -(15 \times 0.3)i \\ = (25v -4.5i) \; kg \; m/s \\ p_f = p_i \\ 25v -4.5i = -5i \\ 25v = -0.5i \\ v = -0.02i$