Question 178252
(a) If the building is 54 ft tall, then 1/2 the
distance to the ground is {{{54/2 = 27}}}ft
The height after {{{t}}} seconds is {{{27}}}ft
{{{h[0] = 54}}}ft
{{{h = -9t^2 + h[0]}}}
{{{27 = -9t^2 + 54}}}
{{{9t^2 = 54 - 27}}}
{{{9t^2 = 27}}}
{{{t^2 = 3}}}
{{{t = sqrt(3)}}}sec
{{{t = 1.732}}}sec
(b)
Falling to ground level,
{{{h = 0}}}ft (the height above ground will be {{{0}}})
and, still,{{{h[0] = 54}}}ft
{{{0 = -9t^2 + 54}}}
{{{9t^2 = 54}}}
{{{t^2 = 6}}}
{{{t = sqrt(6)}}}sec
{{{t = 2.449}}}sec