Question 147563
{{{h(t) = -2.6t^2 + 32.1t + 5.5}}} Start with the given equation.



{{{35 = -2.6t^2 + 32.1t + 5.5}}} Plug in {{{h(t)=35}}}



{{{10(35)=10(-2.6t^2+32.1t+5.5)}}} Multiply both sides by 10 to clear out the decimals.



{{{350=-26t^2+321t+55}}} Distribute and multiply.



{{{0=-26t^2+321t+55-350}}} Subtract 350 from both sides.



{{{0=-26t^2+321t-295}}} Combine like terms.



Let's use the quadratic formula to solve for t



{{{t = (-b +- sqrt( b^2-4ac ))/(2a)}}} Start with the quadratic formula



{{{t = (-(321) +- sqrt( (321)^2-4(-26)(-295) ))/(2(-26))}}} Plug in  {{{a=-26}}}, {{{b=321}}}, and {{{c=-295}}}



{{{t = (-321 +- sqrt( 103041-4(-26)(-295) ))/(2(-26))}}} Square {{{321}}} to get {{{103041}}}. 



{{{t = (-321 +- sqrt( 103041-30680 ))/(2(-26))}}} Multiply {{{4(-26)(-295)}}} to get {{{30680}}}



{{{t = (-321 +- sqrt( 72361 ))/(2(-26))}}} Subtract {{{30680}}} from {{{103041}}} to get {{{72361}}}



{{{t = (-321 +- sqrt( 72361 ))/(-52)}}} Multiply {{{2}}} and {{{-26}}} to get {{{-52}}}. 



{{{t = (-321 +- 269)/(-52)}}} Take the square root of {{{72361}}} to get {{{269}}}. 



{{{t = (-321 + 269)/(-52)}}} or {{{t = (-321 - 269)/(-52)}}} Break up the expression. 



{{{t = (-52)/(-52)}}} or {{{t =  (-590)/(-52)}}} Combine like terms. 



{{{t = 1}}} or {{{t = 295/26}}} Simplify. 



So our answers are {{{t = 1}}} or {{{t = 295/26}}} 



where the second answer approximates {{{t = 11.346}}} 



So when the ball is initially at 35 feet, the time is {{{t = 1}}}.