Chapter 10.4, Problem 5STP

For Exercises 1-6, choose the correct letter.

The pendulum of a cuckoo clock completes one full swing every t seconds.

The variable t is determined by the function $t=2\sqrt{\frac{l}{3.3}}$

where I is the length in meters of the pendulum. Each swing takes 0.5 seconds. How many centimeters long is the pendulum?

A. 20.625 cm B. 41.25 cm C. 82.5 cm D. 330 cm

To determine

To find: that how many cm long is the pendulum when each swing takes $0.5$ seconds.

Answer to Problem 5STP

The pendulum is $20.6\text{cm}$ long when each swing takes $0.5$ seconds.

Explanation of Solution

Given information:

The function is $t=2\sqrt{\frac{l}{3.3}}$ .

Calculation: to find the solution, first substitute and then simplify,

  $\begin{array}{l}t=2\sqrt{\frac{l}{3.3}}\\ 0.5=2\sqrt{\frac{l}{3.3}}\text{ [substitute]}\\ \frac{1}{4}=\sqrt{\frac{l}{3.3}}\text{ [simplify]}\\ \frac{l}{3.3}=\frac{1}{16}\text{ [square]}\\ l=0.206\text{m [simplify]}\\ l=20.6\text{cm [}1\text{m}=\text{100cm]}\end{array}$

Thus, The pendulum is $20.6\text{cm}$ long when each swing takes $0.5$ seconds.