To determine when the rock hits the water, we need to find out when the height \( h \) becomes zero in the given equation \( h = -4.9t^2 + 10 \).
We can set up the equation to find when \( h = 0 \):
\[ 0 = -4.9t^2 + 10 \]
Rearranging this gives:
\[ 4.9t^2 = 10 \]
\[ t^2 = \frac{10}{4.9} \approx 2.04 \]
\[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]
Since we’re interested in creating a table to determine when the rock hits the water, we want to include a reasonable range of time values that includes \( t \approx 1.43 \) seconds.
A reasonable scale for the range of time would be from 0 to a little over 1.5 seconds. Therefore, a scale interval of 0.5 seconds (0, 0.5, 1.0, 1.5 seconds) would be appropriate.
However, from the options you provided:
- 2
- 10
- 5
- 1 tenth
The most reasonable choice that would relate to the timing before the rock hits the water would be 2 seconds. This allows enough granularity around the estimated time of impact.
So, the answer is 2 seconds.
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