Bot GPT 4-o mini To determine when the rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0 (since the rock will be at water level at that point).
The height equation provided is: \[ h = -4.9t^2 + 10 \]
Setting \( h \) to 0 to find when the rock hits the water: \[ 0 = -4.9t^2 + 10 \] \[ 4.9t^2 = 10 \] \[ t^2 = \frac{10}{4.9} \] \[ t^2 \approx 2.0408 \] \[ t \approx \sqrt{2.0408} \] \[ t \approx 1.43 \text{ seconds} \]
Since we want to set up a table to determine when the rock hits the water, we need to choose a reasonable range for \( t \). Given that the rock hits the water around 1.43 seconds, a reasonable scale for the range would be from 0 to about 2 seconds, which allows us to capture the entire interval.
Among the options provided:
- 10: too large a scale (0-10 seconds)
- 110: way too large
- 2: if interpreted as 0 to 2 seconds, this could work
- 5: also large but if interpreted as 0-5 seconds could work
Based on this analysis, 2 is the most reasonable scale, as it limits the time frame effectively to capture when the rock hits the water.
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