The amount of time the ball is in the air before it hits the ground again to the nearest tenth is 3.1seconds
Given the equation modeled by the height expressed as:
h = -16t²+vt + s
Given the following:
Speed v = 48ft/s
Height s = 6feet
Substitute the given parameter into the formula:
h = -16t²+48t + 6
The ball hits the ground when h = 0
The equation then becomes:
-16t²+48t + 6 = 0
Multiplying through by -1 will give:
16t²-48t - 6 = 0
Divide through by 2:
8t²-24t - 3 = 0
Using the general formula:
[tex]t=\frac{-(-24)\pm\sqrt{(-24)^2-4(8)(-3)} }{2(8)} \\t=\frac{24\pm\sqrt{(576+96} }{16}\\t=\frac{24\pm\sqrt{672} }{16} \\t=\frac{24\pm25.92}{16}\\t=\frac{49.92}{16}\\t= 3.12s[/tex]
Hence the amount of time the ball is in the air before it hits the ground again to the nearest tenth is 3.1seconds.
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