13) The graph is a negative parabola. The flare shoots up and gravity pushes it back down. The flare hits the water when the height equals zero. To put it in simple words, you are looking for are the x-intercepts.
h = -16t² + 104t + 56
0 = -16t² + 104t + 56
0 = -8(2t² - 13t - 7)
0 = 2t² - 13t - 7
0 = 2t² + t - 14t - 7
0 = 2t( t + 1) - 7(t + 1)
0 = (2t - 7)(t + 1)
0 = 2t - 7 0 = t + 1
t = [tex]\frac{7}{2}[/tex] = 3.5 t = -1
Since time cannot be negative, disregard t = -1
Answer: t = 3.5 seconds
14) same as #13
h = -16t² + 64t
0 = -16t² + 64t
0 = -16( t² - 4)
0 = t² - 4
0 = (t - 2) (t + 2)
0 = t - 2 0 = t + 2
t = 2 t = -2 (disregard t = -2)
Answer: t = 2
