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

34.5 m at 55.5 degrees above the positive x-axis

Step-by-step 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=√(v_x^2+v_y^2)=√(19.5^2+28.4^2)=34.5 m`

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

`\theta=tan^(-1)((v_y)/(v_x))=tan^(-1) ((28.4)/(19.5))=55.5^(\circ)`