Problem $1$

The plate is attached by a pin at A and a rocker at $B.$ A force $F=-30$hat$()-50$hat$()(lb)$ is applied to the upper right corner of the plate.

A$.$ Replace the two loadings by an equivalent resultant force and specify where the resultant's line of action intersects the bottom edge of the plat along $B.$

B$.$ Solve for the reaction forces at A and $B.$

vec$(30{)}^{150}$

$-100-$Bysin$306+$Bycos$3011$

$F_{By}=50,5F_{By}+3F_{Ax}=100$

$F_{Ax}=F_{Bx}+30$

$F=\sqrt[\phantom{2}]{{30}^2+{50}^2}=10\sqrt[\phantom{2}]{34}(Ib)$

$M=0-100-50$

$]=0|$

$-30,-50,0$

$[11,0,0|=[\frac{650}{-3+\frac{11}{2}\sqrt[\phantom{2}]{3}}$

$A_x=36=6$

Bycos$30-50-Ax=0$

Bysin$30+30=Ay$

$49\mathrm{.}6\frac{1}{2},Ay=79\mathrm{.}8$

$49\mathrm{.}8$