A boy travels 8 km eastward to a point B and then 6km northward to another point C. Determine the difference between the magnitude of displacement of the bo...

A boy travels 8 km eastward to a point B and then 6km northward to another point C. Determine the difference between the magnitude of displacement of the boy and distance travelled by him

Answer Details

To determine the displacement, we need to find the resultant of the two vectors. Using Pythagoras theorem, we can find the magnitude of the resultant vector.

Let's draw a diagram to represent the situation. Let's assume that the starting point is A, the end point is C, and B is the intermediate point.

       6km
         ^
         |
         |
         |
  8km<---C
         |
         |
         |
         A

From the diagram, we can see that the boy has travelled a total distance of 8km + 6km = 14km.

To find the displacement, we can use the Pythagorean theorem:

displacement² = (8km)² + (6km)²

displacement² = 64km² + 36km²

displacement² = 100km²

displacement = 10km

Therefore, the magnitude of the displacement is 10km.

The difference between the magnitude of displacement and distance travelled is:

difference = displacement - distance travelled

difference = 10km - 14km

difference = -4km

Since the displacement is greater than the distance travelled, the boy has some amount of displacement left after travelling the distance. Therefore, the difference is negative, indicating that the magnitude of displacement is 4km less than the distance travelled.

So the answer is -4.0km, but since a negative answer is not one of the options provided, we can assume that the correct answer is 4.0km.