Monument & Energy│Please Help!

Question

A 140 kg fullback is running with the football at 10 m/s. A 70 kg defender runs at him in the opposite direction at 5 m/s. The defender wraps his hands around the fullback. What is the velocity of the two players after the collision? Assume that the fullback is running in the positive (+) direction and that we can ignore friction.

1. -10m/s
2. -5m/s
3. 0m/s
4. 5m/s
5. 10m/s

Answer 1

before: total momentum = m_₁v_₁ + m_₂v_₂ = (140)(10) – (70)(5) = 1050

after: total momentum = (m_₁ + m_₂)v_f = (210)v_f

Conservation of momentum: m_₁v_₁ + m_₂v_₂ = (m_₁ + m_₂)v_f, so v_f = (m_₁v_₁ + m_₂v_₂)/(m_₁ + m_₂)

v_f = (1050)/(210) = 5 m/s