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.

Desmos Link

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

Answer 1

To determine when the rock will hit the bottom of the crevasse, we need to find the time \( x \) when the function \( f(x) = -4.9x^2 + 9 \) equals \(-2\) (since the bottom of the crevasse is 2 meters below ground level). This gives us the equation:

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

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

1. Add \( 2 \) to both sides:

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

which simplifies to:

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

2. Rearranging gives:

\[
4.9x^2 = 11
\]

3. Now, divide both sides by \( 4.9 \):

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

4. Taking the square root of both sides:

\[
x = \sqrt{\frac{11}{4.9}} \approx \sqrt{2.2449} \approx 1.4982
\]

5. Rounding to the nearest tenth gives:

\[
x \approx 1.5
\]

Thus, the rock will hit the bottom of the crevasse in approximately **1.5 seconds**.