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A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 ft/s. The ball's height (in feet) after t seconds is given by the following.
h=5+31t-16t^2

Find all values of t for which the ball's height is 19 feet.
t= _ seconds
Round your answer(s) to the nearest hundredth.
(If there is more than one answer, use the "or" button.)

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 31 fts The balls height in feet after t seconds is given by the following h class=

Respuesta :

Solving a quadratic function, it is found that the ball has a height of 19 feet at t = 0.72 seconds and t = 1.22 seconds.

What is a quadratic function?

A quadratic function is given according to the following rule:

[tex]y = ax^2 + bx + c[/tex]

The solutions are:

  • [tex]x_1 = \frac{-b + \sqrt{\Delta}}{2a}[/tex]
  • [tex]x_2 = \frac{-b - \sqrt{\Delta}}{2a}[/tex]

In which:

[tex]\Delta = b^2 - 4ac[/tex]

In this problem, the function is:

h(t) = -16t² + 31t + 5

The height is of 19 feet when h(t) = 19, hence:

19 = -16t² + 31t + 5

16t² - 31t + 14 = 0.

Then:

  • [tex]\Delta = (-31)^2 - 4(16)(14) = 65[/tex]
  • [tex]x_1 = \frac{31 + \sqrt{65}}{32} = 1.22[/tex]
  • [tex]x_2 = \frac{31 - \sqrt{65}}{32} = 0.72[/tex]

More can be learned about quadratic functions at https://brainly.com/question/24737967

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