Question

While hiking, Julia kicked a small rock off a ledge that was meters above a crevasse. Graph the equation f(x) = −4.9x2+9

. Use the graph to determine when the rock will hit the bottom of the crevasse, 2 meters below ground level. Round your answer to the nearest tenth of a second.

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(1 point)
The rock will hit the bottom of the crevasse in seconds.

Answer 1

To find when the rock will hit the bottom of the crevasse, we need to solve the equation \( f(x) = -4.9x^2 + 9 \) for when \( f(x) = -2 \), since the bottom of the crevasse is 2 meters below ground level.

Set the equation equal to -2:

\[
-4.9x^2 + 9 = -2
\]

Now, let's solve for \( x \):

1. Add 2 to both sides:

\[
-4.9x^2 + 9 + 2 = 0
\]

\[
-4.9x^2 + 11 = 0
\]

2. Rearranging gives:

\[
4.9x^2 = 11
\]

3. Divide by 4.9:

\[
x^2 = \frac{11}{4.9}
\]

4. Taking the square root of both sides:

\[
x = \sqrt{\frac{11}{4.9}} \approx 1.51
\]

5. Rounding to the nearest tenth gives:

\[
x \approx 1.5
\]

Thus, the rock will hit the bottom of the crevasse in approximately \( \mathbf{1.5} \) seconds.