Question

A vector has an x-component of 19.5m and a y-component of 28.4m. Find the magnitude and direction of the vector

Answer 1

Answer:

34.5 m at 55.5 degrees above the positive x-axis

Explanation:

Resolving a vector means finding its components along two perpendicular axis: most commonly, they are chosen as the x and y axis.

In this problem, we have a vector whose components are:

x -component: 19.5 m

y- component: 28.4 m

The two components are perpendicular to each other: this means that we can find the magnitude of the vector by using the Pythagorean theorem

$v=\sqrt{v_x^2+v_y^2}=\sqrt{19.5^2+28.4^2}=34.5 m$

The direction, instead, can be found by using the following formula:

$\theta=tan^{-1}(\frac{v_y}{v_x})=tan^{-1} (\frac{28.4}{19.5})=55.5^{\circ}$