Answer :
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!