+0

# Algebra problem

0
59
1

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

#1
+2
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!

Jan 20, 2022