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A frog with bionic legs leaps from a stump with an initial velocity of 64 ft/sec. It
is determined that the height of the frog as a function of time can by modeled
by h (t) = -16t² +64t + 3. How many seconds will it take for the frog to
land on the ground?

Respuesta :

Considering the given quadratic function, it is found that it will take 4.05 seconds for the frog to land on the ground.

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]

The height after t seconds is given by:

h(t) = -16t² + 64t + 3.

it hits the ground when h(t) = 0, hence:

-16t² + 64t + 3 = 0

16t² - 64t - 3 = 0.

The coefficients are a = 16, b = -64, c = -3, hence:

  • [tex]\Delta = (-64)^2 - 4(16)(-3) = 4288[/tex]
  • [tex]t_1 = \frac{64 + \sqrt{4288}}{32} = 4.05[/tex]
  • [tex]t_2 = \frac{64 - \sqrt{4288}}{32} = -0.05[/tex]

Time has to be positive, hence the frog lands on the ground after 4.05 seconds.

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