Two football players collide head-on in midair while chasing a pass.

- The first player has a mass of 103.5 kg and an initial velocity of 6.30 m/s.
- The second player has a mass of 124 kg and an initial velocity of -5.9 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.)

___ m/s

The velocity of the two football players just after their head-on collision, while they cling together, can be calculated using conservation of momentum. The result is that their combined velocity just after the impact is approximately -0.35 m/s, indicating they move together in the direction the second player was initially moving.

Explanation:

To find the velocity of the two football players just after they collide and cling together, we use conservation of momentum. The total momentum before the collision must equal the total momentum after the collision, assuming there are no external forces acting on the system of the two players. The equation for conservation of momentum is:

m1 * v1 + m2 * v2 = (m1 + m2) * v_final

Plugging in the values given:

103.5 kg * 6.30 m/s + 124 kg * -5.9 m/s = (103.5 kg + 124 kg) * v_final

We get:

652.05 kg·m/s - 731.6 kg·m/s = 227.5 kg * v_final

So:

-79.55 kg·m/s = 227.5 kg * v_final

Therefore:

v_final = -79.55 kg·m/s / 227.5 kg

v_final ≈ -0.35 m/s

The negative sign indicates that the direction of the final velocity is opposite to the direction in which the first player was initially moving. In other words, after the collision, the two players move together in the direction the second player was initially moving.