$6\mathrm{.}24$ You throw a $20\mathrm{.}0-$N rock vertically into the air from ground level. You observe that when it is $15\mathrm{.}1$ m above the ground, it is traveling at $24\mathrm{.}2\frac{m}{s}$ upward. Use the work$-$energy theorem to find $($a$)$ the rock's speed just as it left the ground and $($b$)$ its maximum height.