Final answer:
When two football players of masses 95.0 kg and 115 kg collide with velocities 6.00 m/s and -3.50 m/s respectively and cling together, the final velocity can be calculated using the conservation of momentum. The combined velocity after the collision is approximately 0.798 m/s in the direction of the first player's initial motion.
Step-by-step explanation:
Understanding Inelastic Collisions
When two football players collide, their velocities directly factor into the result of the collision. If a 95.0 kg player with a velocity of 6.00 m/s and a 115 kg player with a velocity of -3.50 m/s collide and cling together, the combined mass post-collision will be the sum of the two players’ mass, which is 210 kg. Using the principle of conservation of momentum, the total momentum before the collision must be equal to the total momentum after the collision. Therefore, the combined velocity just after impact can be calculated using the equation:
(mass1 × velocity1) + (mass2 × velocity2) = (combined mass) × (combined velocity)
(95.0 kg × 6.00 m/s) + (115 kg × -3.50 m/s) = (210 kg) × (combined velocity)
(570 kg·m/s) + (-402.5 kg·m/s) = (210 kg) × (combined velocity)
Combined velocity after impact = 167.5 kg·m/s / 210 kg = 0.798 m/s
The final velocity of the players after they cling together would be approximately 0.798 m/s in the direction of the first player’s initial motion, as positive values indicate the original direction of the first player.