Question

Eric decided to go for a walk from his home. He headed 6 meters east and x meters north. The angle formed by the displacement vector and the horizontal vector is 37°. What is the length of the displacement vector?

Answer 1

The answer is A. 7.5.

Answer 2

Length of displacement vector = 7.51 m

Step-by-step explanation:

Consider east as positive X axis and North as positive Y axis.

Eric headed 6 meters east, Displacement = 6 i

Then he headed X meters north, Displacement = X j

Total displacement = 6 i + X j

Angle it makes with horizontal axis, θ = tan⁻¹(X/6) = 37°

X/6 = tan 37

X = 4.52 m

Total displacement = 6 i + 4.52 j

Magnitude =
`√(6^2+4.52^2) =7.51m`

Length of displacement vector = 7.51 m