Calculating Net Displacement and Direction from a Walking Path

The Physics Problem: Determining Displacement in Vector Terms

Question:

Rick takes a walk, moving 40 meters east, then 50 meters north, and finally 30 meters in a direction 60 degrees east of north. The task is to determine Rick's net displacement and the angle of this displacement from the starting point.

Solution: Vector Analysis of the Path

To solve this problem, we analyze Rick's path using vector addition:

Phase 1 - Breaking Down the Path into Vectors

• Rick's first move (40 meters east) is represented as vector A.
• His second move (50 meters north) is vector B.
• The third move (30 meters at 60 degrees east of north) is vector C.

Phase 2 - Calculating the Vectors

• Vector A (eastward) can be represented as 40i (where i is the unit vector in the east direction).
• Vector B (northward) is 50j (where j is the unit vector in the north direction).
• Vector C needs to be broken down into its eastward and northward components using trigonometry.

Phase 3 - Determining Net Displacement

• The net displacement vector is the sum of vectors A, B, and C.
• We calculate this sum to find the magnitude and direction of the net displacement.

By applying these steps, we can find the total displacement and its angle relative to the starting point, illustrating the application of vector addition in real-world scenarios.