A child wanders down a circular staircase from the top $of$ a tower.

With $x,y,zin$ feet and the origin $at$ the base $of$ the tower,

her position $t$ minutes from the start $is$ given $by$

$x=5cost,y=5sint,z=65-5t$

$(a)$ How tall $is$ the tower?

The height $is$

feet.

$(b)$ How long does $it$ take for the child $to$ reach the bottom?

$It$ takes

minutes.

$(c)$ What $is$ her speed $at$ time $t?$

NOTE: Enter the exact answer, $or$ round $to$ three decimal places.

Her speed $is$

$f\frac{t}{m}in.$

$(d)$ What $is$ her acceleration $at$ time $t?$

vec$(a)=$

vec$(i)+$

vec$(j)+$

vec$(k)$