At time t=0, a ball is thrown downward at 24 feet per second from a height of \(180\) feet above the ground. The equation $h = -16t^2 - 24t +180$ describes the height (in feet) of the ball. In how many seconds will the ball hit the ground? Express your answer as a decimal.

Guest Jan 20, 2022

#1**0 **

Hey there!

I solved this problem using the quadratic formula however I'm sure that you can use other methods of solving a quadratic.

As we are trying to figure out the time that the ball hits the ground we can set \(h\) as equal to \(0\).

\(0=-16^2-24t+180 \)

I decided to divide all of our terms by -4 to give us some easier terms to work with.

\(0=4t^2+6t-45\)

Plugging our numbers into the quadratic formula of \(\frac{-b\pm\sqrt{b^2-4ac}}{2a}\)

\(\frac{-6\pm\sqrt{6^2-(4)(4)(-45)}}{2(4)}\)

After evaluating we get the answer of \(\frac{-3\pm3\sqrt{21}}{4}\)

This can be put in decimal form (rounded to the nearest hundred) as 2.69, or -4.19

Since your answer can't be negative, the ball will hit the ground after 2.69 seconds.

Hope this helps!

AkoCLXXX Jan 20, 2022