Problem $1.(6$ points$)$ The dancer pictured above is holding an arabesque in equilibrium with her stance foot flat $($Image A$)$ and on pointe $($Image B$).$ The arrows on the contralateral leg $($left leg in air$)$ and torso show the locations of the center of mass for her total leg and upper body $($including head and arms$),$ respectively.

$($a$)$ Draw any missing external forces that should be included in this diagram.

$($b$)$ List any assumptions you would make to analyze these two dance positions.

$($c$)$ Are the net joint forces and moments at the dancer's hip equal between Positions A and B$?$ Why or why not?

$($d$)$ Write the equations of equilibrium in vector form for Position A$.$ Clearly define any variables.

$($e$)$ Solve for the location of the head$/$arms$/$trunk centroid location, $\backslash ($ d $\backslash ),$ for Position A and B$.$ Are they different values? Why or why not?

$($f$)$ For Position A $,$ if the right ankle is located at $\backslash ((220,137)\backslash ),$ the right knee at $\backslash ((229,219)\backslash ),$ and the right hip at $\backslash ((208,302)\backslash ),$ calculate the flexion angle of the right knee.