Question

Two football players with mass 85 kg and 110 kg run directly toward each other with speeds 4 m/s and 7 m/s respectively. If they grab each other as they collide, what is the combined speed of the players just after the collision?

Answer 1

Use the conservation of the momentum to answer this question:

$m_1\vec v_1+m_2\vec v_2 = m\vec v\implies\\\vec v = \frac{m_1\vec v_1+m_2\vec v_2}{m_1+m_2}\\v = \frac{85kg\cdot 4 m/s+110kg\cdot (-7m/s)}{195kg}=-2.2\frac{m}{s}$

The resulting speed of the two bodies will be 2.2 m/s in the (original) direction of the overweight guy (110kg). Their brains not happy about the collision either.