A man walks east before proceeding north. If the displacement of the man is 13 meters; 67.38 degrees north of east. What was the distance covered by the man?
N / 13 m = sin(67.38º)
E / 13 m = cos(67.38º)
distance = N + E
To find the distance covered by the man, we need to use the concept of vector addition. Let's break down the given information into two components: the eastward displacement and the northward displacement.
1. Eastward displacement: We know that the man walks east before proceeding north. This means that the eastward displacement is the projection of the total displacement onto the east direction. We can calculate this using trigonometry.
Eastward Displacement = Total Displacement * cos(angle)
Eastward Displacement = 13 meters * cos(67.38 degrees)
Eastward Displacement ≈ 13 meters * 0.3920 (rounded to four decimal places)
Eastward Displacement ≈ 5.096 meters (rounded to four decimal places)
2. Northward displacement: Similarly, the northward displacement is the projection of the total displacement onto the north direction. We can calculate this using trigonometry as well.
Northward Displacement = Total Displacement * sin(angle)
Northward Displacement = 13 meters * sin(67.38 degrees)
Northward Displacement ≈ 13 meters * 0.9199 (rounded to four decimal places)
Northward Displacement ≈ 11.959 meters (rounded to four decimal places)
Now, to find the distance covered by the man, we can use the Pythagorean theorem.
Distance Covered = √(Eastward Displacement^2 + Northward Displacement^2)
Distance Covered = √(5.096^2 + 11.959^2)
Distance Covered ≈ √(25.964416 + 143.049681)
Distance Covered ≈ √(169.014097)
Distance Covered ≈ 13 meters (rounded to two decimal places)
Therefore, the distance covered by the man is approximately 13 meters.