Final Answer:
The components of the displacement vector, which is 34.0 meters in length and directed 60.0 degrees east of north, are 17.0 meters north (^N34.0) and 29.5 meters east (^E34.0).
Step-by-step explanation:
To determine the north and east components of the displacement vector, we use trigonometric functions. Given the vector's length (34.0 meters) and direction (60.0 degrees east of north), we can find its north and east components using basic trigonometry. The north component (N) can be calculated using the formula: N = Displacement × cos(θ), where θ is the angle between the vector and the north direction. Substituting the values, N = 34.0 m × cos(60.0°) = 34.0 m × 0.5 = 17.0 meters.
The east component (E) can be found using the formula: E = Displacement × sin(θ). Substituting the values, E = 34.0 m × sin(60.0°) = 34.0 m × √3 / 2 ≈ 29.5 meters. Therefore, the displacement vector has a north component of 17.0 meters and an east component of 29.5 meters.
These components represent the projection of the vector onto the north and east directions, respectively. They help us understand how much of the overall displacement occurs in each direction. The angle and length of the vector determine these components, allowing us to break down the motion or displacement into its constituent parts along different axes, making it easier to analyze and understand its overall direction and magnitude.