Answer
The bucket was dropped from the top of the 15th floor.
Work Step by Step
let
$H$ = height
$t$ = time
$s(t)$ = the height of the bucket at time t
$s(t)$ = $H - 4.9t^{2}$
t = T-1.5, s(t) = 47.5 m
$s(T-1.5)$ = $H - 4.9(T-1.5)^{2}$
$47.5$ = $H - 4.9(T-1.5)^{2}$ => equation 1
t = T, s(t) = 0 m
$s(T)$ = $H - 4.9(T)^{2}$
$0$ = $H - 4.9(T)^{2}$ => equation 2
solve 2 equations then
T = 3.98 and H = 77.67 m
Floor is 5 m high so
Floor = $\frac{77.67}{5}$ = $15.53$
so The bucket was dropped from the top of the 15th floor.
