$[0\mathrm{.}33/1$ Points$]$ SERCP$118\mathrm{.}3.$P$\mathrm{.}025.$MI$.$

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A $560-N$ uniform rectangular sign $4\mathrm{.}00$ m wide and $3\mathrm{.}00$ m high is suspended from a horizontal, $6\mathrm{.}00-m-$long, uniform, $130-N$ rod as indicated in the figure below. The left end of the rod is supported by a hinge and the right end is supported by a thin cable making a $30\mathrm{.}0$ angle with the vertical. $($Assume the cable is connected to the very end of the $6\mathrm{.}00-m-$long rod, and that there are $2\mathrm{.}00$ m separating the wall from the sign.$)$

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$($a$)$ Find the $($magnitude of the$)$ tension $T$ in the cable.

$50$ N

$($b$)$ Find the horizontal and vertical components of the force exerted on the left end of the rod by the hinge. $($Take up and to the right to be the positive directions. Indicate the direction with the sign of your answer.$)$

horizontal component $$ You appear to have made an error in taking into account the angle that the cable makes with respect to the wall. N

vertical component

Make sure you have included all the forces that contribute to the force on the hinge. N

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