Final answer:
The final velocity of the football players after the collision is calculated using conservation of linear momentum. Considering their masses and initial velocities, and assuming no external forces, the final velocity of both players clinging together is approximately 0.31 m/s toward west.
Step-by-step explanation:
To calculate the final velocity of the players after they collide and fall together, we can use the principle of conservation of linear momentum. The total momentum before the collision must equal the total momentum after the collision if there are no external forces acting on the system.
The momentum of the first player is the product of their mass and velocity, which is 75 kg × 2 m/s = 150 kg·m/s toward west. The second player has a momentum of 70 kg × 1.5 m/s = 105 kg·m/s toward east. Since they are running in opposite directions, the momentum of the second player is negative when combined, which yields a total initial momentum of 150 kg·m/s - 105 kg·m/s = 45 kg·m/s toward west.
After the collision, both players move together, so their combined mass is 75 kg + 70 kg = 145 kg. Let's call the final velocity v_f. To find the final velocity, we use the equation:
Initial total momentum = Final total momentum
(75 kg × 2 m/s) + (70 kg × -1.5 m/s) = 145 kg × v_f
45 kg·m/s = 145 kg × v_f
Dividing both sides by 145 kg, we get:
v_f = 45 kg·m/s / 145 kg
v_f = 0.3103 m/s toward west.
Therefore, the final velocity of the players after the collision is approximately 0.31 m/s toward west.