FluffyLizard26
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Lugi is trying to hit a turtle shell. The height of
Lugi's feet above the ground is given by the
functionh(t) = -16t² +961 + 2.
How long does it take for Lugi to hit the shell on the ground?
A. 3 seconds
B. 146 seconds
0.6.02 seconds
D. 16 seconds

Lugi is trying to hit a turtle shell The height of Lugis feet above the ground is given by the functionht 16t 961 2 How long does it take for Lugi to hit the sh class=

Respuesta :

MrRoyal

Answer:

C. 6.02sec

Step-by-step explanation:

Given

[tex]h(t) = -16t\² +96t + 2[/tex]

Required

Time to hit the ground

When the turtle shell hits the ground, [tex]h(t) = 0[/tex]

So:

[tex]0 = -16t\² +96t + 2.[/tex]

Solving using quadratic formula:

[tex]t = \frac{-b\±\sqrt{b^2-fac}}{2a}[/tex]

Where:

[tex]a = -16; b =96; c = 2[/tex]

So:

[tex]t = \frac{-96\±\sqrt{96^2-4 * -16 * 2}}{2*-16}[/tex]

[tex]t = \frac{-96\±\sqrt{9344}}{-32}[/tex]

[tex]t = \frac{-96\±96.66}{-32}[/tex]

Split:

[tex]t = \frac{-96+96.66}{-32}[/tex] or [tex]t = \frac{-96-96.66}{-32}[/tex]

[tex]t = \frac{0.66}{-32}[/tex] or  [tex]t = \frac{-192.66}{-32}[/tex]

[tex]t = -0.020625[/tex] or  [tex]t = 6.020625[/tex]

So time can't be negative, we have:

[tex]t = 6.020625[/tex]

Option C answers the question

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