In a free$-$fall experiment, an object is dropped from a height of $h=576$ feet. A camera on the ground $500$ ft from the point

$($a$)$ Find the position function that yields the height of the object at time $t,$ assuming the object is released at time $t=0.($Use $32f\frac{t}{se{c}^2}$ for the acceleration due to gravity.$)$

$h(t)=$

$$

At what time $($in sec $)$ will the object reach ground level? $($Round your answer to three decimal places.$)$

$t=sec$

$($b$)$ Find the rates of change $($in $ra\frac{d}{sec})$ of the angle of elevation of the camera when $t=1$ and $t=2.($Round your answers to four decimal places.$)$

${}^{\text{'}}(1)=,ra\frac{d}{sec}$

${}^{\text{'}}(2)=,ra\frac{d}{sec}$