To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0 (i.e., when the rock reaches the lake). The equation that models the situation is:
\[ h = -4.9t^2 + 10 \]
Setting \( h \) to 0 gives us:
\[ 0 = -4.9t^2 + 10 \]
Rearranging the equation:
\[ 4.9t^2 = 10 \] \[ t^2 = \frac{10}{4.9} \] \[ t^2 \approx 2.0408 \] \[ t \approx \sqrt{2.0408} \approx 1.43 \text{ seconds} \]
Since the rock hits the water at approximately 1.43 seconds, a reasonable scale for the range (time in seconds) in a table would be one that captures this timing effectively.
Looking at the provided options:
- 1tenth (which means using increments of 0.1 seconds) would allow for a very fine scale.
- 2 seconds might also be reasonable since it covers the 1.43 seconds mark comfortably.
The best reasonable scale for the range would likely be 1 tenth (0.1 seconds), as it gives more detail around the time when the rock hits the water. However, 2 seconds would also work but may not provide as much granularity as the tenths.
Therefore, the most suitable choice from the provided options is: 1 tenth.