Final answer:
The velocity of the two football players just after impact, if they cling together, is -1.18 m/s. This result is obtained by applying the principle of conservation of momentum to the combined system of the two players.
Step-by-step explanation:
The subject of this question is Physics, and it is appropriate for a High School level class. The question involves the concept of conservation of momentum, which applies when two football players collide and cling together in midair. Conservation of momentum states that the total momentum of a system remains constant if no external forces act on it. Since the players cling together after the collision, we consider them as a single system with a combined mass equal to the sum of their individual masses.
To find the velocity of the players just after impact, we apply the principle of conservation of momentum. The initial momentum of the system is the sum of the momenta of the two players before the collision. The formula to calculate this is:
Initial momentum = (mass of player 1 × velocity of player 1) + (mass of player 2 × velocity of player 2)
Using the provided data, the initial momentum is as follows:
Initial momentum = (101.5 kg × 4.40 m/s) + (120 kg × -5.9 m/s)
Initial momentum = 446.6 kg·m/s - 708 kg·m/s
Initial momentum = -261.4 kg·m/s
Since the players cling together, their combined mass is (101.5 kg + 120 kg) = 221.5 kg. The final velocity of the system (the two players together) can be calculated by dividing the total initial momentum by the combined mass:
Final velocity = Total initial momentum / Combined mass
Final velocity = -261.4 kg·m/s / 221.5 kg
Final velocity = -1.18 m/s
The negative sign indicates the direction of the final velocity is opposite to the direction of the first player's initial velocity. Therefore, after the collision, the players will be moving together at a velocity of -1.18 m/s, which means in the direction of the second player's initial approach.