Question

While hiking, Julia kicked a small rock off a ledge that was meters above a crevasse. Use GeoGebra to graph the situation using the formula y=−4.9t2+9
𝑦
=
−
4.9
𝑡
2
+
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 rock will hit the bottom of the crevasse in blank seconds.

Answer 1

To find out when the rock will hit the bottom of the crevasse using the equation \( y = -4.9t^2 + 9 \), we want to set \( y \) equal to -2 (since the bottom of the crevasse is 2 meters below ground level).

So we set up the equation:

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

Now, we can solve for \( t \):

\[
-4.9t^2 + 9 + 2 = 0
\]
\[
-4.9t^2 + 11 = 0
\]
\[
4.9t^2 = 11
\]
\[
t^2 = \frac{11}{4.9}
\]
\[
t^2 \approx 2.2449
\]
\[
t \approx \sqrt{2.2449} \approx 1.5
\]

Rounding to the nearest tenth of a second, we find that:

The rock will hit the bottom of the crevasse in approximately **1.5 seconds**.