An object is thrown upwards with initial velocity $w$ meters per second from a point $d$ meters above the ground. Assume that the acceleration due to gravity is -9.8 meters per second squared, and let $v(t)$ and $s(t)$ denote the velocity and position of the object above the ground, respectively, after $t$ seconds.

(a) Determine a function that describes the velocity $v$ of the object after time $t$.

$v(t) =$

(b) Determine a function that describes the position $s$ of the object after time $t$.

$s(t) =$

(c) Use (a) and (b) to obtain a formula that relates the velocity $v$ of the object with $w$, $s$, and $d$. Your formula should have the form $v^2 = \cdots$

$v^2 =$