To solve this problem, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant unless acted on by an external force. In this case, the initial momentum of the fullback before the collision is 75 kg * 10 m/s = 750 kgm/s, and the initial momentum of the lineman before the collision is 100 kg * -4 m/s = -400 kgm/s (since he is moving in the opposite direction). After the collision, the two players stick together and move with a combined mass of 75 kg + 100 kg = 175 kg. Since the total momentum of the system must remain constant, the combined velocity of the two players after the collision must be equal to the total initial momentum of the fullback and lineman before the collision, or 750 kgm/s - 400 kgm/s = 350 kg*m/s.
Therefore, the combined velocity of the two players after the collision is 350 kg*m/s / 175 kg = 2 m/s. This is the speed at which the two players move after the collision. Note that this is much slower than the initial speeds of either player before the collision, which is expected since the combined mass of the two players is greater than the mass of either player alone, and the momentum of the system must be conserved.