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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The rock will hit the bottom of the crevasse in
seconds.
Question 12
11.

1 answer

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.