To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) is zero (i.e., when the rock reaches the lake's surface).
The equation given is:
\[ h = -4.9t^2 + 10 \]
To find when the rock hits the water, we set \( h = 0 \):
\[ 0 = -4.9t^2 + 10 \]
Rearranging gives:
\[ 4.9t^2 = 10 \]
Dividing both sides by 4.9:
\[ t^2 = \frac{10}{4.9} \approx 2.0408 \]
Taking the square root:
\[ t \approx \sqrt{2.0408} \approx 1.43 , seconds \]
Now, we can consider reasonable scales for the range of \( t \). Given that we want to generate a table for \( t \), we should include values around 0 and up to around 1.5 seconds.
Let's evaluate the options for the scale:
- a. 5 - This would result in a very large range unnecessarily since values like 5 seconds are far beyond when the rock will hit the water.
- b. 1/10 - This scale (0.1) would provide very detailed increments, allowing us to capture the moment the rock hits the water accurately.
- c. 2 - This could fit, but 2 seconds is still larger than the actual time we calculated (1.43 seconds).
- d. 10 - Similar to option A, this scale is much too large; we won't need such a range of time.
Given these evaluations, the best reasonable scale for the range is b. 1/10, allowing for a detailed view of the rock's descent and the time it hits the water.