⦁ A running back has a momentum of 110 kg⋅m/s (p1) as he dives east toward the end zone. A linebacker coming in the opposite direction (west) has a momentum of 120 kg⋅m/s (−p2) . When the linebacker collides with the running back, what is the total momentum?
The momentum of an object is a vector quantity, meaning it has both magnitude and direction. In this case, the running back's momentum is in the positive direction (east), while the linebacker's momentum is in the negative direction (west).
To calculate the total momentum, we add the momenta of the two players together. Since the linebacker's momentum is in the opposite direction, we can subtract it from the running back's momentum:
Total momentum = p1 + (-p2)
Substituting the given values:
Total momentum = 110 kg⋅m/s + (-120 kg⋅m/s)
To simplify, we can add the magnitudes first and then determine the final direction:
Total momentum = |110 kg⋅m/s| + |-120 kg⋅m/s| = 110 kg⋅m/s + 120 kg⋅m/s
Now, we have to consider the direction of the total momentum. Since the linebacker's momentum is in the negative direction (west), it subtracts from the running back's momentum (east). Therefore, the final direction will be determined by the greater of the two magnitudes.
Since 120 kg⋅m/s > 110 kg⋅m/s, the total momentum will have a magnitude of 120 kg⋅m/s. However, it will be in the direction of the linebacker's momentum, which is west.
Thus, the total momentum is 120 kg⋅m/s in the west direction.