Two football players collide head-on in midair while chasing a pass. The first player has a mass of 102.5 kg and an initial velocity of 6.40 m/s, while the second player has a mass of 112 kg and an initial velocity of -5.7 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.)

The velocity of the players just after impact, when they cling together, is approximately 0.0764 m/s in the direction of the first player's initial velocity. We can apply the principle of conservation of momentum.

To determine the velocity of the football players just after impact, we can apply the principle of conservation of momentum. According to this principle, the total momentum before the collision is equal to the total momentum after the collision.

Given:

Mass of the first player (m1) = 102.5 kg

The initial velocity of the first player (v1i) = 6.40 m/s

Mass of the second player (m2) = 112 kg

The initial velocity of the second player (v2i) = -5.7 m/s

Using the conservation of momentum equation:

(m1 * v1i) + (m2 * v2i) = (m1 + m2) * vf

Substituting the given values:

(102.5 kg * 6.40 m/s) + (112 kg * -5.7 m/s) = (102.5 kg + 112 kg) * vf

(656 kg·m/s) + (-639.6 kg·m/s) = (214.5 kg) * vf

16.4 kg·m/s = 214.5 kg·vf

Dividing both sides by 214.5 kg:

vf = 16.4 kg·m/s / 214.5 kg

vf ≈ 0.0764 m/s

Therefore, the velocity of the players just after impact, when they cling together, is approximately 0.0764 m/s in the direction of the first player's initial velocity.

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