To fill in the missing values of [tex]\( t^2 \)[/tex] for the heights 50.0 cm, 60.0 cm, and 70.0 cm, we need to square the given times associated with these heights. Here are the detailed steps for each:
1. Height: 50.0 cm
- Given time, [tex]\( t = 0.319 \)[/tex] seconds.
- Calculating [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = (0.319)^2
\][/tex]
[tex]\[
t^2 \approx 0.102 \, \text{s}^2
\][/tex]
- So, for height 50.0 cm, [tex]\( t^2 \approx 0.102 \)[/tex].
2. Height: 60.0 cm
- Given time, [tex]\( t = 0.349 \)[/tex] seconds.
- Calculating [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = (0.349)^2
\][/tex]
[tex]\[
t^2 \approx 0.122 \, \text{s}^2
\][/tex]
- So, for height 60.0 cm, [tex]\( t^2 \approx 0.122 \)[/tex].
3. Height: 70.0 cm
- Given time, [tex]\( t = 0.378 \)[/tex] seconds.
- Calculating [tex]\( t^2 \)[/tex]:
[tex]\[
t^2 = (0.378)^2
\][/tex]
[tex]\[
t^2 \approx 0.143 \, \text{s}^2
\][/tex]
- So, for height 70.0 cm, [tex]\( t^2 \approx 0.143 \)[/tex].
Now, filling in these values in Table 2.2:
\begin{tabular}{|c|c|c|}
\hline Height, [tex]$h( \pm 0.1 \, \text{cm})$[/tex] & Time, [tex]$t( \pm 0.001 \, \text{s})$[/tex] & [tex]$t^2\left(\text{s}^2\right)$[/tex] \\
\hline 10.0 & 0.141 & 0.020 \\
\hline 20.0 & 0.200 & 0.040 \\
\hline 30.0 & 0.247 & 0.061 \\
\hline 40.0 & 0.284 & 0.081 \\
\hline 50.0 & 0.319 & 0.102 \\
\hline 60.0 & 0.349 & 0.122 \\
\hline 70.0 & 0.378 & 0.143 \\
\hline
\end{tabular}
