A rock is thrown off a cliff at an angle of $58$ above the horizontal. The cliff is $145$ m high. The initial speed of the rock is $20$ m$/$s$.($Assume the height of the thrower is negligible.$)$

$($a$)$

How high above the edge of the cliff does the rock rise $($in m$)?$

$14\mathrm{.}7$ m

$($b$)$

How far has it moved horizontally when it is at maximum altitude $($in m$)?$

$18\mathrm{.}3$ m

$($c$)$

How long after the release does it hit the ground $($in s$)?$

$7\mathrm{.}44$ s

$($d$)$

What is the range of the rock $($in m$)?$

$78\mathrm{.}9$ m

$($e$)$

What are the horizontal and vertical positions $($in m$)$ of the rock relative to the edge of the cliff at

t $=2\mathrm{.}0$ s$,$

t $=4\mathrm{.}0$ s$,$

and

t $=6\mathrm{.}0$ s$?$

$($Assume the $+$x$-$direction is in the horizontal direction pointing away from the cliff, the $+$y$-$direction is up towards the sky$,$ and x $=$ y $=0$ at the point from which the rock is thrown.$)$