Santa Claus is going down a chimney as shown. He has reduced the amount the is pushing against the walls of the chimney such that he is about to stip. Let Santa's mass be m $,$ the coefficient of static friction between his shoes and chimney be Us$1$ and the coefficient of static friction between his back and chimney be Us$2.$

If a problem says "variables only", this means you should answer in terms of m$,$ Us$1,$ Us$2,$ and any fundamental constants.

a$)$ Draw and label a free$-$body diagram of the forces acting on Santa.

b$)$ Write Newton's $2^{nd}$ law for the forces acting on Santa Claus in both the $x$ and $y$ directions

c$)$ Show that the amount Santa pushes against the chimney with his feet is equal to the amount he pushes against the chimney with his back. $($variables only$)$

d$)$ Solve for the magnitude of Santa's push against the chimney. $($variables only$)$

e$)$ Suppose $m=91kg,Us1=1\mathrm{.}2$ and Us$2=0\mathrm{.}80.$ Now solve for Santa's against the chimney,

Using the same values, solve for the magnitude of the friction force between Santa's shoes and chimney,

g$)$ Using again these same values, solve for the magnitude of the friction force between Sante's back and the chimney,

b$)$ BONUS; how long did it take for Boots the Housecat to knock ever the plate of cookies and drink Santa's milk before Santa gver got down the chimney? Assume that the plate and glass are located close to the entrange to the chimney, Bopts weighs $36$ N $,$ the milk is locelly$-$sourced organis whole milk $(3\mathrm{.}5\%$ standard milk fat$),$ and the ceokies are chocolate chip,