Final answer:
Using conservation of momentum, the final velocity of two colliding football players is calculated to be 1.852 m/s East. Momentum is the product of mass and velocity, and it remains unchanged in a closed system without external forces.
Step-by-step explanation:
To determine the velocity of the players after the collision, we can use the principle of conservation of momentum. The total momentum before the collision must equal the total momentum after the collision assuming the system is closed and there are no external forces. The momentum of a body is given by the product of its mass and velocity.
We first establish the direction to be positive, let's say the East direction is positive. Thus, the velocity of the second player will be negative since he is traveling West. Now, we compute the initial momentum of both players:
- Player 1: m1 * v1 = 109 kg * 7.2 m/s = 784.8 kg·m/s East
- Player 2: m2 * v2 = 191 kg * -1.2 m/s = -229.2 kg·m/s West
The total initial momentum is then 784.8 kg·m/s + (-229.2 kg·m/s) = 555.6 kg·m/s East.
After the collision, the two players move together in the same direction, so their combined mass is m1 + m2 = 109 kg + 191 kg = 300 kg. Let's denote the final velocity of both players as vf. The total final momentum is (m1 + m2) * vf = 300 kg * vf.
Since momentum is conserved, we can equate the initial momentum to the final momentum:
555.6 kg·m/s = 300 kg * vf
Dividing both sides by 300 kg, we find vf = 555.6 kg·m/s / 300 kg = 1.852 m/s East.
So, the final velocity of the players moving together after the collision is 1.852 m/s East.