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Suppose an egg is thrown off the top of a building 240 feet above ground. The height, h, in feet of the rock above the ground is given by h = −16t2 + 60t + 240, where t is the time in seconds. How long does it take the egg to hit the ground? A) 2.4 seconds B) 3.4 seconds C) 4.8 seconds D) 6.2 seconds

Answer :

mixter17

Hello!

The answer is: D) 6.2 seconds

Why?

When the egg hit the ground,  the height will be equal to 0, so, from the given equation we need to find the roots or zeroes.

It's a quadratic function, we can find the roots using the quadratic equation:

[tex]\frac{-b+-\sqrt{b^{2}-4ac}}{2a}[/tex]

So, from the given function we know that:

[tex]a=-16\\b=60\\c=240[/tex]

So, substituting we have:

[tex]\frac{-60+-\sqrt{60^{2}-4*(-16)*240}}{2*(-16)}=\frac{-60+-\sqrt{3600+15360}}{-32}\\\\\frac{-60+-\sqrt{18960}}{-32}=\frac{-60+-(137.69)}{-32}[/tex]

[tex]x1=\frac{-60-137.69}{-32}=6.18[/tex]

[tex]x2=\frac{-60+137.69}{-32}=-2.42[/tex]

So, since the time can not be a negative value, the correct option is:

6.18≈6.2 seconds

Hence, it takes 6.2 seconds to the egg to hit the ground.

Have a nice day!

tongcreator

5.7 is not an answer choice, so 6.2

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