A hunter $,$ armed with a bow and an arrow,is standing on a cliff that is $6$ metres above ground level $.$ He spots an eagle flying horizontally at a height of $14,5$ metres above ground level $.$ He then shoots the arrow at the eagle $.$The flight path of the arrow is defined as h$($t$)=-5$t$^2+13$t$+6,$ where h represents the distance $,$in metres $,$ above ground level and t elapsed, in seconds, after the arrow is shot $.$ Will the arrow hit the eagle $?$ Support your answer with necessary calculations.