Final answer:
After a head-on collision where two soccer players come to a complete stop and one player's mass is 1.2 times that of the other, the player with less mass must have had a greater initial speed to offset the larger mass of the other player, according to the conservation of momentum.
Step-by-step explanation:
If two soccer players collide head-on and are stopped, and one player has a mass that is 1.2 times the mass of the other player, the conclusion about their initial speeds can be drawn from the principle of conservation of momentum. In a system where two objects collide and come to a complete stop, the total momentum before the collision must be zero immediately after the collision as well (provided the collision is in an isolated system without external forces). Since momentum is the product of mass and velocity (p=mv), and the momentum of the system before collision is equal to the sum of the momenta of the two players, the player with larger mass must have a smaller speed compared to the player with lesser mass to ensure their momenta cancel each other out.
For example, in a scenario where one player's mass is m and the other's is 1.2m, for them to come to a stop after a head-on collision, the ratio of their velocities before the collision must be inverse to the ratio of their masses. That is, their initial speeds must have been such that v1 * m = -1.2m * v2, where v1 and v2 are the initial velocities of the lighter and heavier players, respectively. This relationship implies that the lighter soccer player was moving faster initially if they stopped completely after the collision.