While hiking, Julia kicked a small rock off a ledge that was meters above a crevasse. Use the Texas Desmos calculator to graph the situation using the formula y=−4.9t2+9.

Question

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.



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

Answer 1

To find when the rock hits the bottom of the crevasse, we can use the provided equation:

\[ y = -4.9t^2 + 9 \]

Here, \(y\) represents the height of the rock above ground level at time \(t\) seconds. Since the bottom of the crevasse is 2 meters below ground level, we want to find when \(y = -2\).

Setting the equation equal to -2 gives us:

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

Now, we solve for \(t\):

1. Rearranging the equation:

\[ -4.9t^2 + 9 = -2 \] \[ -4.9t^2 = -2 - 9 \] \[ -4.9t^2 = -11 \] \[ 4.9t^2 = 11 \]

2. Dividing both sides by 4.9:

\[ t^2 = \frac{11}{4.9} \] \[ t^2 \approx 2.2449 \]

3. Taking the square root:

\[ t \approx \sqrt{2.2449} \approx 1.5 \]

Rounding to the nearest tenth gives:

\[ t \approx 1.5 \text{ seconds} \]

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