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.
Question 12
11.

Answer 1

To determine when the rock will hit the bottom of the crevasse, we need to find the time \( x \) at which the height \( f(x) \) is equal to -2 meters (since the bottom of the crevasse is 2 meters below ground level).

The equation given is:

\[
f(x) = -4.9x^2 + 9
\]

We set this equal to -2:

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

Now we solve for \( x \):

\[
-4.9x^2 + 9 + 2 = 0
\]
\[
-4.9x^2 + 11 = 0
\]
\[
-4.9x^2 = -11
\]
\[
x^2 = \frac{11}{4.9}
\]
\[
x^2 \approx 2.2449
\]
\[
x \approx \sqrt{2.2449}
\]
\[
x \approx 1.5
\]

So the rock will hit the bottom of the crevasse at approximately **1.5 seconds**.

The answer is that the rock will hit the bottom of the crevasse in **1.5 seconds**.