Question

why is it -16 in the formula: h=-16^2+vt+c

Answer 1

because gravity sucks

Answer 2

gravity is the second derivative of the position, aka acceleration and is a constant at \(-32\) feet per second per second (per second squared is the usual way to say this)
so it is always true that
\(h''(t)=-32\)
hence \(h'(t)=-32t+C\) first derivative is velocity, so this says
\[v(t)=-32t+C\] and the C is your initial velocity, what you get when you replace t by 0 hence \(C=v_0\)

Answer 3

take anti derivatives once more to get
\[h(t)=-16t^2+v_0t+D\] and again D is your initial height, what you get when you replace t by 0 hence the formula
\[h(t)=-16t^2+v_0t+h_0\]

Answer 4

if you have not gotten to calculus yet, however, and were just told the formula, you have to take it on faith. like the existence of god.