To determine when the rock hits the water using the equation \( h = -4.9t^2 + 10 \), we need to find the time \( t \) when \( h = 0 \) (the height of the water).
Setting up the equation:
\[ 0 = -4.9t^2 + 10 \]
Rearranging gives:
\[ 4.9t^2 = 10 \]
Dividing both sides by 4.9:
\[ t^2 = \frac{10}{4.9} \approx 2.0408 \]
Then taking the square root:
\[ t \approx \sqrt{2.0408} \approx 1.43 \text{ seconds} \]
Now, to set up a table to determine when the rock hits the water, we can choose a scale for the time \( t \) that includes the time up to when the rock hits the water.
Since the rock hits the water at approximately \( t = 1.43 \) seconds, a reasonable scale for the range of time could be from \( 0 \) to about \( 2 \) seconds, allowing us to see the entire motion of the rock as it falls.
A possible table setup could include time intervals such as \( 0 \), \( 0.5 \), \( 1.0 \), \( 1.5 \), and \( 2.0 \) seconds.
Here's an example of how the table might look:
| Time (t) | Height (h) | |----------|------------| | 0.0 | 10.0 | | 0.5 | 6.23 | | 1.0 | 5.0 | | 1.5 | 0.2 | | 2.0 | -9.8 |
You can calculate the height at each of these time points using the given equation. This table will help visualize when the rock hits the water as well.
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