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
seconds.

Answer 1

To find out when the rock hits the bottom of the crevasse, we need to solve the equation

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

for \(y = -2\) (since the bottom of the crevasse is 2 meters below ground level, which is at 0). Therefore, we set the equation equal to -2 and solve for \(t\):

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

First, we can simplify this by adding 2 to both sides:

\[
-4.9t^2 + 11 = 0
\]

Now, rearranging gives:

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

Dividing both sides by -4.9:

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

Calculating \(t^2\):

\[
t^2 \approx 2.2449
\]

Taking the square root of both sides gives:

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

Therefore, rounding to the nearest tenth, the rock will hit the bottom of the crevasse in:

\[
\boxed{1.5} \text{ seconds.}
\]