Question #9a724

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Answer 1 · 2018-02-06T22:40:56

#3.5s#

graph{-16x^2+54x+7 [-5, 5, -5, 5]}

when the ball hits the ground, its height is #0#.

#h(t) = 0#

this means that #-16t^2 + 54t + 7 = 0#.

#(8t+1)(2t-7) = 16t - 56t + 2t - 7 = 16t - 54t - 7#

#-(8t+1)(2t-7) = -16t + 54t + 7#

factorising gives #-(8t+1)(2t-7) = 0#.

#0 = -0#

#(8t+1)(2t-7)=0#.

#8t = -1# or #2t = 7#

#t = -1/8# or #t = 7/2#

note that the answer asks for the height after #t# seconds. this means that only the positive solution of #t# applies.

here, this is #7/2#

#7/2 = 3.5#

#3.5# seconds after being thrown up from #7# feet above ground, the ball will reach the ground again (assuming that the ground is level).