$2.$ In the figure below, a single frictionless roller$-$coaster car of mass $\backslash (\backslash$mathrm$\{$m$\}=825\backslash$mathrm$\{$~kg$\}\backslash )$ tops the first hill with speed $\backslash (\backslash$mathrm$\{$v$\}\_\{0\}=17\mathrm{.}0\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at height $\backslash (\backslash$mathrm$\{$h$\}=42\mathrm{.}0\backslash$mathrm$\{$~m$\}\backslash ).$ How much work does the gravitational force do on the car from that point to $($a$)$ point A $,($b$)$ point B $,$ and $($c$)$ point C$?$ If the gravitational potential energy of the car $-$ Earth system is taken to be zero at $\backslash ($ C $\backslash ),$ what is its value when the car is at $($d$)$ B and $($e$)$ A$?($f$)$ If mass $\backslash ($ m $\backslash )$ were doubled, would the change in the gravitational potential energy of the system between points A and B increase, decrease, or remain the same?

Problem$-2$