Does displacement always have to include angles and direction? For example a man travels 3 m (N) and 4m (E). Can you just put 5m for displacement or do you have to put the angle and direction? Explain why.
Displacement is a vector quantity that represents the overall change in position of an object. It includes both magnitude (or size) and direction. In the scenario you mentioned, where a person travels 3 meters north and 4 meters east, the displacement cannot be simply represented by a single value of 5 meters.
To accurately represent the displacement, we need to consider both the magnitudes and the directions of the displacements in the north and east directions. Using the Pythagorean theorem, we can find the magnitude of the displacement:
Magnitude of displacement = √[(3m)^2 + (4m)^2] = √(9m^2 + 16m^2) = √(25m^2) = 5m
This shows that the magnitude of the displacement is indeed 5 meters. However, to fully describe the displacement, we also need to include the direction. In this case, we can use trigonometry to find the angle.
The angle can be found by taking the inverse tangent (arctan) of the ratio of the north displacement to the east displacement:
Angle = arctan(3m/4m) ≈ 36.87°
Therefore, the complete representation of the displacement in this scenario is a magnitude of 5 meters and an angle of approximately 36.87 degrees.
Including both the magnitude and the angle is important because it provides a more precise and comprehensive description of the displacement. It allows us to understand not only how far an object has moved but also in which direction it has moved relative to a reference point or axis.