To determine when the rock hits the water, we need to find out when the height \( h \) is equal to 0 (the height of the lake). The equation provided is:
\[ h = -4.9t^2 + 10 \]
Setting this equation to 0 gives:
\[ 0 = -4.9t^2 + 10 \]
Solving for \( t \):
\[ 4.9t^2 = 10 \] \[ t^2 = \frac{10}{4.9} \approx 2.04 \] \[ t \approx \sqrt{2.04} \approx 1.43 \text{ seconds} \]
Now, let's consider the reasonable scale for the range of a table that indicates time in seconds until the rock hits the water. Since the rock hits the water at approximately 1.43 seconds, choosing a range that comfortably accommodates this time is important.
The suggested options for scale could be based on round numbers that cover the time interval. Among the given options:
- A scale of 2 would cover from 0 to 2 seconds, which is reasonable.
- A scale of 5 would cover from 0 to 5 seconds, which is also reasonable but beyond what's necessary for just 1.43 seconds.
The best choice that directly suits the time when the rock hits the water would be:
2.
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