To find the momentum of the system after the collision, we need to determine the total momentum of both players before the collision. The momentum \( p \) of an object is given by the formula:
\[ p = mv \]
where \( m \) is the mass and \( v \) is the velocity.
Step 1: Calculate the momentum of each player before the collision.
- Player 1 (mass = 105 kg, velocity = 8.6 m/s):
\[ p_1 = m_1 v_1 = 105 , \text{kg} \times 8.6 , \text{m/s} = 903 , \text{kg} \cdot \text{m/s} \]
- Player 2 (mass = 90 kg, velocity = -9.0 m/s):
\[ p_2 = m_2 v_2 = 90 , \text{kg} \times (-9.0 , \text{m/s}) = -810 , \text{kg} \cdot \text{m/s} \]
Step 2: Calculate the total momentum before the collision.
\[ p_{\text{total}} = p_1 + p_2 = 903 , \text{kg} \cdot \text{m/s} + (-810 , \text{kg} \cdot \text{m/s}) = 903 , \text{kg} \cdot \text{m/s} - 810 , \text{kg} \cdot \text{m/s} = 93 , \text{kg} \cdot \text{m/s} \]
Step 3: Determine the momentum of the system after the collision.
In an isolated system, the total momentum before the collision is equal to the total momentum after the collision (conservation of momentum). Since we have calculated that the total momentum before the collision is \( 93 , \text{kg} \cdot \text{m/s} \), the total momentum of the system after the collision will also be \( 93 , \text{kg} \cdot \text{m/s} \).
Conclusion:
The momentum of the system after the football players collide is:
\[ \boxed{93 , \text{kg} \cdot \text{m/s}} \]
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