Final answer:
The defender's momentum is 200 kgm/s west, and the striker's is resolved into 207.8 kgm/s east and 120 kgm/s north. Therefore, the eastward momentum after the tackle is 7.8 kgm/s, and the northward momentum is 120 kgm/s. The magnitude of the total momentum is approximately 120.6 kgm/s.
Step-by-step explanation:
The total momentum of the two football players can be determined by finding the vector sum of each player's momentum. The defender's momentum is straightforward to calculate since he is moving directly west, so his momentum would be the product of his mass and velocity. For the defender, momentum = mass × velocity = 100 kg × (2 m/s west) = 200 kgm/s west.
For the striker, it's essential to resolve his momentum into horizontal and vertical components because he is moving in a direction 30° north of east. His total momentum would be mass × velocity = 80 kg × (3 m/s 30° north of east). The horizontal (eastward) component is 80 kg × 3 m/s × cos(30°) = 207.8 kgm/s east, and the vertical (northward) component is 80 kg × 3 m/s × sin(30°) = 120 kgm/s north. The total momentum must consider both components, so we have a resulting vector with a horizontal of 207.8 kgm/s east subtracting the defender's 200 kgm/s west, and a vertical of 120 kgm/s north.
Thus, the eastward momentum after the tackle is 207.8 kgm/s - 200 kgm/s = 7.8 kgm/s east, and the northward momentum remains 120 kgm/s north unchanged. The total momentum is the vector sum of eastward and northward components.
The magnitude of the total momentum is calculated using Pythagorean theorem: √(7.8² + 120²) kgm/s ≈ √14545.64 kgm/s ≈ 120.6 kgm/s. Since none of the given options matches this value, it appears there might be a problem with the provided options or the interpretation of the question.