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Two football players collide head-on in midair while chasing a pass. The first player has a 105.5 kg mass and an initial velocity of 4.80 m/s, while the second player has a 119 kg mass and initial velocity of -3.4 m/s. What is their velocity (in m/s) just after impact if they cling together? (Indicate the direction with the sign of your answer.)

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Answer:

To find the velocity just after impact when the two football players collide and cling together, we can use the principle of conservation of momentum.

The momentum of an object is the product of its mass and velocity. According to the conservation of momentum, the total momentum before the collision should be equal to the total momentum after the collision.

Let's denote the velocity just after impact as "v". The momentum of the first player before the collision is given by (mass of first player * initial velocity of first player), and the momentum of the second player before the collision is given by (mass of second player x initial velocity of second player).

The total momentum before the collision is therefore:

(mass of first player x initial velocity of first player) + (mass of second player x initial velocity of second player)

= (105.5 kg x 4.80 m/s) + (119 kg x -3.4 m/s)

To find the total mass of the players after collision, we sum their masses:

Total mass after collision = mass of first player + mass of second player

= 105.5 kg + 119 kg

Now, using the conservation of momentum, the total momentum after the collision should be equal to the total momentum before the collision:

Total momentum after collision = Total mass after collision x velocity after collision

Therefore:

(mass of first player x initial velocity of first player) + (mass of second player * initial velocity of second player) = (Total mass after collision x velocity after collision)

(105.5 kg x 4.80 m/s) + (119 kg x -3.4 m/s) = (Total mass after collision x velocity after collision)

Now, we can solve for the velocity after collision:

(105.5 kg x 4.80 m/s) + (119 kg x -3.4 m/s) = (Total mass after collision x velocity after collision)

Solving this equation will give us the velocity after collision, and the sign of the answer will indicate the direction.

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