Question

Neil rides his long board to Physics class. He travels 8 m east the 4 m north. What distance did he cover? Please include the number and unit. What was the magnitude of his displacement? Please include the number and unit. What was the direction of his displacement? Please abbreviate (N, S, E, W, etc.)

Answer 1

Neil covered a total distance of 12 m and the magnitude of his displacement is 8.94 m, approximately 26.57° north of east.

Step-by-step explanation:

When dealing with vectors and displacements, we can break down each segment of Neil's travel into components and then use these to find the total distance covered and the magnitude of his displacement. Neil travels 8 m east and then 4 m north. The total distance covered is simply the sum of these individual distances, which is 8 m + 4 m = 12 m. However, displacement, being a vector quantity, requires us to consider both the magnitude and direction, which can be found using the Pythagorean theorem.

The magnitude of his displacement is √(8² + 4²) = √(64 + 16) = √80 = 8.94 m (to two decimal places). To find the direction, we use the tangent function: tan(θ) = opposite/adjacent = 4/8 = 0.5, which gives us an angle θ = arctan(0.5). This angle is approximately 26.57° north of east (to two decimal places).