Question 166107
First, you need to find the height (s) from which the bottle was dropped.
{{{s = 4(12)}}} This is 4 storeys times 12 ft per storey.
{{{s = 48}}}feet.
The observer is 6 feet tall, so you want to find the time, t, at which the bottle reaches a height of 6 feet when dropped from a height (s) of 48 feet.
Starting with:
{{{h(t) = s-16t^2}}} Substitute h = 6 ft. and s = 48 ft.
{{{6 = 48-16t^2}}} Add {{{16t^2}}} to both sides.
{{{16t^2+6 = 48}}} Subtract 6 from both sides.
{{{16t^2 = 42}}} Divide both sides by 16.
{{{t^2 = 42/16}}} Now take the square root of both sides.
{{{t = sqrt(42/16)}}} Simplify the right side.
{{{t = 6.48/4}}}
{{{t = 1.6}}} seconds.