Problem $4.(1$ point$)$

A yoga ball $\backslash (($m$=0\mathrm{.}56\backslash$mathrm$\{$~kg$\})\backslash )$ is thrown downwards onto a spring $(\backslash ($ k$=67\backslash$mathrm$\{$~N$\}/\backslash$mathrm$\{$m$\}\backslash )).$

It leaves the throwers hand $\backslash (\backslash$mathrm$\{$d$\}=2\mathrm{.}1\backslash$mathrm$\{$~m$\}\backslash )$ above the top of the spring travelling at $\backslash (10\mathrm{.}3\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash ).$ There is air resistance, and it is found that $4\mathrm{.}3$ J is lost during the fall and interaction with the spring. The top of the spring is itself $\backslash (\backslash$mathrm$\{$d$\}=2\mathrm{.}1\backslash$mathrm$\{$~m$\}\backslash )$ above the ground.

$($a$)$ How much is the spring compressed when the ball is at its lowest point?

$($b$)$ How high does the ball rise above the ground after it leaves the spring? $($Assume that another $4\mathrm{.}3$ J is lost again.$).$