Question

A force vector has a magnitude of 584 newtons and points at an angle of 38o below the positive x axis. What are (a) the x scalar component and (b) the y scalar component of the vector

Answer 1

Answer:

a) The x scalar component of the vector is 460.198 Newtons

b) The y scalar component of the vector is 359.54 Newtons.

Explanation:

The given vector is represented in coordinate axis in the attached figure

We have

$\overrightarrow{F}_{x}=|F|cos(\theta )\widehat{i}\\\\\overrightarrow{F}_{x}=584cos(38^{o})\widehat{i}\\\\\overrightarrow{F}_{x}=460.198\widehat{i}$

Similarly we have

$\overrightarrow{F}_{y}=|F|sin(\theta )\widehat{-j}\\\\\overrightarrow{F}_{y}=-584sin(38^{o})\widehat{j}\\\\\overrightarrow{F}_{y}=-359.54\widehat{j}$