Respuesta :
Answer:
The height of the rugby ball is 45 feet at t = 1.27s and t = 2.17s
Step-by-step explanation:
The height of the ball, in feet, after t seconds, is given by the following equation:
[tex]h(t) = -16t^{2} + 55t + 1[/tex]
When the height of the rugby ball is 45 feet
This is t for which: h(t) = 45
So
[tex]h(t) = -16t^{2} + 55t + 1[/tex]
[tex]45 = -16t^{2} + 55t + 1[/tex]
[tex]-16t^{2} + 55t - 44 = 0[/tex]
Solving a quadratic equation:
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 = a(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} - 4ac[/tex]
In this question:
[tex]-16t^{2} + 55t - 44 = 0[/tex]
So [tex]a = -16, b = 55, c = -44[/tex]
[tex]\bigtriangleup = 55^{2} - 4*(-16)*(-44) = 209[/tex]
[tex]t_{1} = \frac{-55 + \sqrt{209}}{2*(-16)} = 1.27[/tex]
[tex]t_{2} = \frac{-55 - \sqrt{209}}{2*(-16)} = 2.17[/tex]
The height of the rugby ball is 45 feet at t = 1.27s and t = 2.17s
