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

Accepted Solution

Hello!The answer is: D) 6.2 secondsWhy?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 secondsHence, it takes 6.2 seconds to the egg to hit the ground.Have a nice day!