Use the worked example above to help you solve this problem. A stone is thrown from the top of a building with an initial velocity of $20\mathrm{.}1\frac{m}{s}$ straight upward, at an initial height of $53\mathrm{.}8m$ above the ground. The stone just misses the edge of the roof on its way down, as shown in the figure.

$($a$)$ Determine the time needed for the stone to reach its maximum height.

$s$

$($b$)$ Determine the maximum height.

$m$

$($c$)$ Determine the time needed for the stone to return to the height from which it was thrown, and the velocity of the stone at that instant.

$\backslash$table$[[$Time$,,s$