Q:

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

A:
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!