The total momentum before and after the collision must be conserved.
The total momentum before the collision is:
[tex]p_i = m_1 v_1 + m_2 v_2[/tex]
where m1 and m2 are the masses of the two players, and [tex]v_1 [/tex] and [tex]v_2[/tex] their initial velocities. Both are considered with positive sign, because the two players are running toward the same direction.
The final momentum is instead
[tex]p_f = (m_1+m_2)v_f[/tex]
because now the two players are moving together with a total mass of (m1+m2) and final speed vf.
By requiring that the momentum is conserved
[tex]p_i=p_f[/tex]
we can calculate vf, the post-collision speed:
[tex]m_1 v_1 + m_2 v_2 = (m_1+m_2)v_f[/tex]
[tex]v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 +m_2}= \frac{(98 kg)(8.6 m/s)+(76 kg)(9.8m/s)}{98 kg+76 kg}=9.1 m/s [/tex]
and the direction is the same as the direction of the players before the collision.
