Question

A vector has an x-component
of 6.15 m and a y-component
of -3.88 m.
Find the direction of the vector.

Answer 1

Answer:

$-32.2^{\circ}$

Explanation:

A vector is said to be resolved if it is expressed in terms of 2 components along 2 perpendicular axes, generally chosen as the x- and y- direction of the Cartesian plane.

The components of a vector are given by

$v_x = v cos \theta\\v_y = v sin \theta$

where

v is the magnitude of the vector

$\theta$ is the angle that the vector makes with the x-axis

By dividing the second equation by the  first one, we get:

$tan \theta = \frac{v_y}{v_x}$

In this problem, we have:

$v_x = 6.15 m$ is the x-component of the vector

$v_y = -3.88 m$ is the y-component of the vector

Solving for $\theta$, we can find the direction of the vector:

$\theta= tan^{-1}(\frac{v_y}{v_x})=tan^{-1}(\frac{-3.88}{6.15})=-32.2^{\circ}$

where the negative sign means below the x-axis.