To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) is 0 (meaning the rock has reached the surface of the lake). The equation given is:
\[ h = -4.9t^2 + 10 \]
Setting \( h = 0 \):
\[ 0 = -4.9t^2 + 10 \]
To solve for \( t \):
\[ 4.9t^2 = 10 \]
\[ t^2 = \frac{10}{4.9} \]
\[ t^2 \approx 2.0408 \]
\[ t \approx \sqrt{2.0408} \]
\[ t \approx 1.43 \text{ seconds} \]
Now, to set up a table that calculates the height of the rock over time, we need to consider a range for \( t \) that includes values from 0 to slightly higher than 1.43 seconds.
A reasonable scale for the range (considering our maximum time of around 1.43 seconds) could be increments of 0.1 seconds, as this would provide a detailed view of the rock's height as it falls.
Thus, based on the given options, 1/10 (0.1 seconds) would be the most reasonable scale for the range when setting up a table to determine when the rock hits the water.
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