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.

 Jan 20, 2022

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. 




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




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!

 Jan 20, 2022

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