To determine when the rock hits the water, we need to find out when the height \( h \) reaches 0, which represents the level of the lake. The equation given is:
\[ h = -4.9t^2 + 10 \]
Setting \( h \) to 0 gives:
\[ 0 = -4.9t^2 + 10 \]
Solving for \( t \):
\[ 4.9t^2 = 10 \]
\[ t^2 = \frac{10}{4.9} \]
\[ t^2 \approx 2.04 \]
\[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]
Now, to determine a reasonable scale for the table to track time, we want a range that includes 0 seconds to approximately 1.5 seconds.
Considering the options provided:
- 1/10: This scale would give you a table with many entries, which might be more than needed.
- 1: This would give you entries for 0, 1, 2 seconds, which fits within the range and gives a clear understanding of when the rock hits the water.
- 10: This would be too large for the range.
- 5: Also too large for the given range of about 1.5 seconds.
- 2: This scale would include times 0, 2 seconds, which again does not provide enough detail around the time of impact.
Since we need to closely observe the time it takes for the rock to hit the water (approximately 1.43 seconds), the most reasonable scale for your table is 1 (each entry representing 1 second).
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