Final answer:
The displacement in the east and north directions is calculated using trigonometric functions, based on the total displacement and the angle given (40° north of east). The total displacement is the original vector with its given magnitude and direction, and there is no displacement in the south direction for the described scenario.
Step-by-step explanation:
The student's question is related to calculating the displacement components and resultant displacement of a hiker walking in a specific direction. Displacement is a vector quantity that represents the change in position of an object and has both magnitude and direction. Here's how to calculate the east and north components of the displacement:
- (a) To calculate the displacement in the east direction, use the cosine function for the angle given (which is 40° north of east). The eastward displacement (De) is calculated using the formula De = D * cos(θ), where D is the total displacement and θ is the angle.
- (b) To calculate the displacement in the north direction, use the sine function. The northward displacement (Dn) is calculated as Dn = D * sin(θ).
For these calculations, we use the total displacement of 4.5 km and an angle of 40°:
- De = 4.5 km * cos(40°)
- Dn = 4.5 km * sin(40°)
(c) The total displacement is the vector sum of the east and north components, which in this case, asingle vector pointing 40° north of east with a magnitude of 4.5 km, so no additional calculation is needed unless the components are meant to be combined for another vector sum.
(d) There is no displacement in the south direction as the hiker is moving north of east.