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.