Question $1$:

Sir Lance a Lost's new draw bridge was designed poorly and stops at an angle of $20$ below the horizontal. Sir Lost and his steed stop when their combined center of mass is $1\mathrm{.}0m$ from the end of the bridge. The bridge is $8\mathrm{.}0m$ long and has a mass of $2000kg$; the lift cable is attached to the bridge $5\mathrm{.}0m$ from the castle end and to a point $12m$ above the bridge. Sir Lost's mass combined with his armor and steed is $1000kg.$

$($a$)$ Use the related quantities sensemaking technique to compare the combined gravitational force acting on Sir Lance a Lost, his armor, and his steed $($treat these as one object$)$ with the normal and frictional forces from the bridge acting on his steed.

$($b$)$ Determine the tension in the cable.

$($c$)$ Find the horizontal and vertical force components acting on the bridge at the castle end.