Question

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 1

5.7 is not an answer choice, so 6.2

Answer 2

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:

`\frac{-b+-\sqrt{b^(2)-4ac}}{2a}`

So, from the given function we know that:

`a=-16\\b=60\\c=240`

So, substituting we have:

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

`x1=(-60-137.69)/(-32)=6.18`

`x2=(-60+137.69)/(-32)=-2.42`

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!