Question 605863
{{{H= -16t^2+80t+576}}}


{{{300 = -16t^2+80t+576}}}


{{{0 = -16t^2+80t+576-300}}}


{{{0 = -16t^2+80t+276}}}


{{{-16t^2+80t+276 = 0}}}


{{{16t^2-80t-276 = 0}}}


Now use the quadratic formula to solve


{{{t = (-b+-sqrt(b^2-4ac))/(2a)}}}


{{{t = (-(-80)+-sqrt((-80)^2-4(16)(-276)))/(2(16))}}}


{{{t = (80+-sqrt(6400-(-17664)))/(32)}}}


{{{t = (80+-sqrt(24064))/32}}}


{{{t = (80+sqrt(24064))/32}}} or {{{t = (80-sqrt(24064))/32}}}


{{{t = (80+16*sqrt(94))/32}}} or {{{t = (80-16*sqrt(94))/32}}}


{{{t = (5+sqrt(94))/2}}} or {{{t = (5-sqrt(94))/2}}} <font color="blue"><--- Exact Solutions</font>


{{{t = 7.34767985741632}}} or {{{t = -2.34767985741632}}} <font color="red"><--- Approximate Solutions</font>



We now ignore the negative solution since a negative time value doesn't make any sense.



So the ball is 300 ft above the ground at approximately <font color="red">7.34767985741632</font> seconds