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

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

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

Step-by-step 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}`