Question

PROBLEM SOLVING The period of a pendulum is the time the pendulum takes to complete one back-and-forth swing. The period $T$ (in seconds) can be modeled by the function $T=1.1\sqrt{L}$ , where $L$ is the length (in feet) of the pendulum. Estimate the length of a pendulum with a period of $1.65$ seconds. Write your answer as a decimal.

Answer 1

If $T=1.65$ seconds, then we can solve the equation for $L$ as follows:

$$

T=1.1\sqrt{L}

$$

$$

\frac{T}{1.1}=\sqrt{L}

$$

$$

\left(\frac{T}{1.1}\right)^2=L

$$

Substituting $T=1.65$, we get:

$$

L=\left(\frac{1.65}{1.1}\right)^2=2.25

$$

Therefore, the length of the pendulum is approximately 2.25 feet.