Final answer:
To find the velocity after the collision, we need to apply the law of conservation of momentum. The collision involves a 92 kg fullback running at 5 m/s and colliding with a 75 kg linebacker moving at 6 m/s. By calculating the total momentum before the collision and dividing it by the combined mass of the players, we can determine that the velocity after the collision is approximately 5.45 m/s.
Step-by-step explanation:
The law of conservation of momentum states that the total momentum before the collision is equal to the total momentum after the collision.
The momentum of an object is the product of its mass and velocity.
Using this information, we can calculate the velocity after the collision:
Calculate the total momentum before the collision by multiplying the mass of each player by their respective initial velocities.
Add the individual momenta of the players.
Since the players cling together, their combined mass is the sum of their individual masses.
Divide the total momentum by the combined mass to find the velocity after the collision.
In this case, we have a fullback with a mass of 92 kg and initial velocity of 5 m/s, colliding with a linebacker with a mass of 75 kg and initial velocity of 6 m/s.
Using the steps outlined above, we can calculate the velocity after the collision:
Let's calculate the momentum of each player:
Fullback momentum: 92 kg * 5 m/s = 460 kg·m/s
Linebacker momentum: 75 kg * 6 m/s = 450 kg·m/s
Now, let's calculate the total momentum before the collision by adding the individual momenta:
Total momentum before collision:
460 kg·m/s + 450 kg·m/s = 910 kg·m/s
Since the players cling together, their combined mass is the sum of their individual masses:
Combined mass:
92 kg + 75 kg = 167 kg
Finally, we can calculate the velocity after the collision by dividing the total momentum by the combined mass:
Velocity after collision = Total momentum / Combined mass
Velocity after collision = 910 kg·m/s / 167 kg
≈ 5.45 m/s