Question

Consider the vector b⃗ with magnitude 4.00 m at an angle 23.5∘ north of east. what is the x component bx of this vector? express your answer in meters to three significant figures.

Answer 1

Decomposing the vector b on the x-axis and the y-axis, we get a rectangle triangle where the two sides are bx (x-axis) and by (y-axis), and b is the hypothenuse.
The component in x, bx, is equal to the product between the hypothenuse and the cosine of the angle between b and the x-axis, which is $23.5 ^{\circ}$:
$b_x = b \cos (23^{\circ})=(4.00 m)(\cos (23^{\circ}))=3.68 m$