Use the position function $s(t)=-16t^2+v_{0}t+s_0$ for free$-$falling objects.

A ball is thrown straight down from the top of a $800-$foot building with an initial velocity of $-40$ feet per second.

$($a$)$ Determine the position and velocity $v(t)$ functions for the ball.

$s(t)=$

$v(t)=$

$$

$$

$($b$)$ Determine the average velocity, in feet per second, on the interval $1,3.$

$f\frac{t}{s}$

$($c$)$ Find the instantaneous velocities, in feet per second, when $t=1$ and $t=3.$

$v(1)=,f\frac{t}{s}$

$v(3)=,f\frac{t}{s}$

$($d$)$ Find the time, in seconds, required for the ball to reach ground level. $($Round your answer to three decimal places.$)$

$$ s

$($e$)$ Find the velocity of the ball, in feet per second, at impact. $($Round your answer to one decimal place.$)$

$f\frac{t}{s}$