PROBLEM $13\mathrm{.}170$

The Mars Pathfinder spacecraft used large airbags to cushion its impact with the planet's surface when landing. Assuming the spacecraft had an impact velocity of $\backslash (18\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ at an angle of $\backslash (45^\{\backslash$circ$\}\backslash )$ with respect to the horizontal, the coefficient of restitution is $0\mathrm{.}85$ and neglecting friction, determine $($a$)$ the height of the first bounce, $(\backslash ($ b $\backslash ))$ the length of the first bounce. $($Acceleration of gravity on the Mars $\backslash (=3\mathrm{.}73\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash ).$