Question

force f has a magnitude of 475 n acting 140° from the horizontal.
x - y coordinate system
determine the scalar components of f in the x and y directions.
$f_x = square$
$f_y = square$
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Explanation:

Step1: Recall component - formula

The formula for the x - component of a vector $\vec{F}$ with magnitude $F$ and angle $\theta$ from the horizontal is $F_x = F\cos\theta$, and for the y - component is $F_y=F\sin\theta$. Here, $F = 475$ N and $\theta=140^{\circ}$.

Step2: Calculate the x - component

$F_x = 475\times\cos(140^{\circ})$. Since $\cos(140^{\circ})\approx - 0.766$, then $F_x=475\times(- 0.766)=-364.85$ N.

Step3: Calculate the y - component

$F_y = 475\times\sin(140^{\circ})$. Since $\sin(140^{\circ})\approx0.643$, then $F_y = 475\times0.643 = 305.425$ N.

Answer:

$F_x=-364.85$ N, $F_y = 305.425$ N