To solve this problem, we need to analyze the equation \( f(x) = -4.9x^2 + 9 \). This equation represents the height of the rock above the ground in meters, where \( x \) is the time in seconds.
We want to find out when the rock hits the bottom of the crevasse, which is 2 meters below ground level. Therefore, we need to find the value of \( x \) when the height \( f(x) \) equals -2 meters.
Setting the equation equal to -2:
\[ -4.9x^2 + 9 = -2 \]
Now, we can move -2 to the left side of the equation:
\[ -4.9x^2 + 9 + 2 = 0 \]
This simplifies to:
\[ -4.9x^2 + 11 = 0 \]
Now, we can isolate \( x^2 \):
\[ -4.9x^2 = -11 \] \[ x^2 = \frac{11}{4.9} \]
Calculating the right side:
\[ x^2 \approx \frac{11}{4.9} \approx 2.2449 \]
Now, taking the square root of both sides:
\[ x \approx \sqrt{2.2449} \approx 1.5 \text{ seconds} \]
Rounding to the nearest tenth, the rock will hit the bottom of the crevasse in approximately \( 1.5 \) seconds.
Thus, the final answer is:
The rock will hit the bottom of the crevasse in 1.5 seconds.