Question

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.
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**.