The problem is about a directly proportional variation between T and the square root of L.
[tex]T=k\cdot\sqrt[]{L}[/tex]Where k is the constant of proportionality. Let's use L = 7ft and T = 2.9 sec to find k.
[tex]2.9=k\cdot\sqrt[]{7}\to k=\frac{2.9}{\sqrt[]{7}}\approx1.10[/tex]The constant of proportionality is 1.10.
Then, use the constant to find the period of a pendulum that is 10 feet long.
[tex]T=1.10\sqrt[]{10}\approx3.5\sec [/tex]The period of a pendulum that is 10 ft long is 3.5 seconds.
Then, use T = 2 sec to find the length.
[tex]\begin{gathered} 2=1.10\sqrt[]{L} \\ L=(\frac{2}{1.10})^2 \\ L\approx3.3ft \end{gathered}[/tex]The length of a pendulum that beats seconds is 3.3 feet.
