You take a walk in the park for 16.6 steps using a compass that points 25º North – Free B15
Question:
You take a walk in the park for 16.6 steps using a compass that points 25° North of East. How would you use the simulation to represent your path?
Answer:
➤ Define the Coordinate Axes:
- Let the positive x-axis represent East.
- Let the positive y-axis represent North.
➤ Representing the Walk as a Vector:
Your 16.6 steps at 25° North of East can be represented by a vector with:
- Magnitude: 16.6 steps
- Angle: 25° with the positive x-axis (East)
➤ Calculate the Components:
Using trigonometry, the components of the displacement vector are:
Horizontal (Eastward) Component: x = 16.6 × cos(25°)
Vertical (Northward) Component: y = 16.6 × sin(25°)
These components represent how far you move in the East and North directions respectively.
➤ Setting Up the Simulation:
- Place your starting point at the origin (0, 0).
- Draw a vector from the origin to the point
(16.6 × cos(25°), 16.6 × sin(25°)). - Label the vector with its length (16.6 steps) and direction (25° North of East).
➤ Interpreting the Result:
The arrow you’ve drawn represents your path. The tip of the arrow shows your final position relative to your starting point.
This visualization helps you clearly see how both direction and magnitude determine your overall displacement.