To find the length $L$ of the pendulum, we can start by using the formula given for the period $T$:

$T = 2\pi \sqrt{\frac{L}{32}}$

We are given:

• The period $T = 16.2$ seconds
• $\pi = 3.14$

Our goal is to find $L$.

Step 1: Substitute the known values into the formula

$16.2 = 2 \cdot 3.14 \cdot \sqrt{\frac{L}{32}}$

Step 2: Simplify the expression

First, calculate $2 \cdot 3.14$:

$2 \cdot 3.14 = 6.28$

Substituting this into the equation:

$16.2 = 6.28 \cdot \sqrt{\frac{L}{32}}$

Step 3: Isolate the square root

Divide both sides by 6.28:

$\frac{16.2}{6.28} = \sqrt{\frac{L}{32}}$

$2.579 = \sqrt{\frac{L}{32}}$

Step 4: Square both sides to eliminate the square root

$(2.579)^2 = \frac{L}{32}$

$6.651 = \frac{L}{32}$

Step 5: Solve for $L$

Multiply both sides by 32 to solve for $L$:

$L = 6.651 \cdot 32$

$L = 212.832$

Conclusion

The length of the pendulum is approximately:

$\boxed{212.8 \text{ feet}}$

Would you like further details or have any questions?

Here are some related questions you might explore:

1. How does the period of a pendulum change if the length is doubled?
2. What is the effect of changing the acceleration due to gravity on the period of a pendulum?
3. How can this formula be used to measure gravitational acceleration on different planets?
4. How would the period change if the pendulum were shorter or longer?
5. What assumptions are made when using this formula to calculate the period of a pendulum?

Tip: Always keep track of your units when solving problems involving physical quantities to ensure consistency and accuracy.