Miguel does not score after colliding with Joey as the conservation of momentum dictates that they will both be at a standstill post-collision, since their momenta before the collision are equal and opposite.
To determine whether Miguel scores after colliding with Joey, we must consider the conservation of momentum, assuming that external forces are negligible during the collision. Using the formula for conservation of momentum, which is:
Total Momentum before Collision = Total Momentum after Collision.
The total momentum before the collision can be calculated by adding the momentum of each player (momentum = mass × velocity).
For Miguel: momentum = 100 kg × 9.0 m/s = 900 kg·m/s
For Joey: momentum = 75 kg × 12 m/s = 900 kg·m/s (in the opposite direction).
Since the momentum is equal and opposite, and they collide head-on, the total momentum before the collision is zero. After the collision, their combined mass will have a velocity such that the momentum remains zero. Therefore, after the collision, Miguel and Joey will be at a standstill and Miguel will not score.