To determine when Marek's rock hits the water, we need to find the time \( t \) when the height \( h \) becomes 0 (i.e., when the rock reaches the surface of the lake). The equation given is:
\[ h = -4.9t^2 + 10 \]
Setting \( h = 0 \) to find the time of impact:
\[ 0 = -4.9t^2 + 10 \]
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 of both sides:
\[ t \approx \sqrt{2.0408} \approx 1.43 \text{ seconds} \]
Given that the time it takes for the rock to reach the water is approximately 1.43 seconds, a reasonable scale for the range of \( t \) in the table could be from 0 seconds to about 2 seconds.
A suggested table scale could involve increments of 0.2 seconds, allowing you to observe the height of the rock at multiple time points leading up to when it hits the water. Here's a possible scale:
- 0.0 seconds
- 0.2 seconds
- 0.4 seconds
- 0.6 seconds
- 0.8 seconds
- 1.0 seconds
- 1.2 seconds
- 1.4 seconds
- 1.6 seconds
- 1.8 seconds
- 2.0 seconds
This scale allows for a comprehensive view of the rock's height as it falls, especially as it approaches the water.
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