A uniform horizontal sign post has a mass M and length L, and is fixed at one end to a vertical pole. A support cable, which makes an angle theta with the horizontal, stabilizes the sign post. A bird of mass $m$ lands on the post, positioned a distance $x$ from the pole. Determine the vertical and horizontal components of the force exerted by the sign post on its fixed point (pole) as a function of $x$ .

• A. $F_{\text{vert }}=mg\left(\frac{x}{L}\right)+Mg;\ F_{\text{horiz }}=\frac{mg}{L\sin \theta }x+\frac{Mg}{\tan \theta }$
• B. $F_{\text{vert }}=mg\left(1-\frac{x}{L}\right)+\frac{1}{2}Mg;\ F_{\text{horiz }}=\frac{mg}{L\tan \theta }x+\frac{Mg}{2\tan \theta }$
• C. $F_{\text{vert }}=mg\left(\frac{x}{L}\right)+\frac{1}{2}Mg;\ F_{\text{horiz }}=\frac{mg}{L\tan \theta }x+\frac{Mg}{\tan \theta }$
• D. $F_{\text{vert }}=mg\left(2-\frac{x}{L}\right)+\frac{1}{2}Mg;\ F_{\text{horiz }}=\frac{mg}{L\cos \theta }x+\frac{Mg}{2\cos \theta }$

Answer: (B)