Question

while hiking, Julia kicked a small rock off a ledge that was meters above a crevasse. use the Texas Demos calculator to graph the situation using the formula y=-4.9t^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.
The rocket will hit the bottom of the crevasse in ______ seconds.

Answers

Answered by GPT-4o mini
To determine when the rock will hit the bottom of the crevasse using the formula \( y = -4.9t^2 + 9 \), we first need to set \( y \) to the height of the bottom of the crevasse, which is 2 meters below ground level. Since the initial height is 9 meters above the ground, the equation becomes:

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

Now, rearranging the equation gives:

\[
-4.9t^2 + 9 + 2 = 0
\]

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

Next, we isolate \( t^2 \):

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

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

Now we can calculate \( t^2 \):

\[
t^2 \approx 2.2449
\]

Taking the square root of both sides to find \( t \):

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

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

Rounding to the nearest tenth of a second, the answer is:

**The rock will hit the bottom of the crevasse in 1.5 seconds.**
There are no human answers yet. A form for humans to post answers is coming very soon!

Related Questions