Question 304649
When {{{t = 1}}} sec
{{{S(t)= -16t^2 - 32t + 128}}}
{{{S(1)= -16*1^2 - 32*1 + 128}}}
{{{S(1) = -16 - 32 + 128}}}
{{{S(1) = 80}}}
The height above ground is 80 ft
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When {{{S(t) = 0}}} (the height above ground is zero)
{{{-16t^2 - 32t + 128 = 0}}}
Solve using quadratic formula
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{a = -16}}}
{{{b = -32}}}
{{{c = 128}}}
{{{t = (-(-32) +- sqrt( (-32)^2-4*(-16)*128 ))/(2*(-16)) }}}
{{{t = (32 +- sqrt(1024 + 8192 ))/(-32) }}}
{{{t = (32 +- sqrt( 9216 ))/(-32) }}}
{{{t = (32 +- 96)/(-32) }}}
{{{t = (32 - 96)/(-32)}}}
{{{t = (-64)/(-32)}}}
{{{t = 2}}}
In 2 sec the wrench will reach the ground