Question 333790
Given:
{{{S(t) = -16t^2-32t+128}}}
To find the height after 1 second, substitute S = 1 and solve.
{{{S(1) = -16(1)^2-32(1)+128}}} Solve for S.
{{{S(1) = -16-32+128}}} simplify.
{{{S(1) = -48+128}}}
{{{S(1) = 80}}}
The wrench's height is 80 ft. after 1 second.
To find how long it takes for the wrench to reach the ground (height = 0), set the given equation equal to zero and solve for t.
{{{0 = -16t^2-32t+128}}} Factor out -16 to simplify this quadratic equation a bit.
{{{-16(t^2+2t-8) = 0}}} Now solve:
{{{t^2+2t-8 = 0}}} Factor.
{{{(t-2)(t+4) = 0}}} Apply the zero products rule.
{{{t-2 = 0}}} or {{{t+4 = 0}}} so...
{{{highlight(t = 2)}}} or {{{cross(t = -4)}}} Discard the solution since the time, t, will be positive.
The wrench will hit the ground iin 2 seconds.