Respuesta :
Answer:
It will take 0.72s for the football to hits the ground.
Step-by-step explanation:
We have that the equaation for the height of the football is
[tex]H(t) = -16t^{2} + 6t + 4[/tex]
The football will hit the ground when [tex]H(t) = 0[/tex].
[tex]H(t) = -16t^{2} + 6t + 4[/tex]
[tex]-16t^{2} + 6t + 4 = 0[/tex]
Multiplying by -1
[tex]16t^{2} - 6t - 4 = 0[/tex]
To solve this equation, we need the bhaskara formula:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = (x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4a[/tex]
In this problem, we have that:
[tex]16t^{2} - 6t - 4 = 0[/tex]
So
[tex]a = 16, b = -6, c = -4[/tex]
[tex]\bigtriangleup = (-6)^{2} - 4*16*(-4) = 292[/tex]
[tex]t_{1} = \frac{-(-6) + \sqrt{292}}{2*16} = 0.72[/tex]
[tex]t_{2} = \frac{-(-6) - \sqrt{292}}{2*16} = -0.35[/tex]
It cannot take negative seconds for the ball to hit the ground.
So it will take 0.72s for the football to hits the ground.
