Question 1173412
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To answer the problem's question, you need to solve this equation

    -16t^2 + 32t + 20 = 0


and take its larger root.


The equation is equivalent to

    4t^2 - 8t - 5 = 0


Use the quadratic formula

    t = {{{(8 +- sqrt(8^2 -4*4*(-5)))/(2*4)}}} = {{{(8 +- sqrt(144))/8}}} = {{{(8 +- 12)/8}}}.


The larger root is  {{{(8 + 12)/8}}} = {{{20/8}}} = 2.5 seconds.


<U>ANSWER</U>.  The ball will hit the ground in 2.5 seconds.
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Solved.