Sample Problem $11\mathrm{.}2$

You throw a ball vertically upward with a velocity of $\backslash (10\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}\backslash )$ from a window located $20$ m above the ground. Knowing that the acceleration of the ball is constant and equal to $\backslash (9\mathrm{.}81\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$s$\}^\{2\}\backslash )$ downward, determine $($a$)$ the velocity $\backslash ($ v $\backslash )$ and elevation $\backslash ($ y $\backslash )$ of the ball above the ground at any time $\backslash ($ t $\backslash ),($b$)$ the highest elevation reached by the ball and the corresponding value of $\backslash ($ t $\backslash ),($c$)$ the time when the ball hits the ground and the corresponding velocity. Draw the $\backslash ($ v$-$t $\backslash )$ and $\backslash ($ y$-$t $\backslash )$ curves.