Chapter 12, Problem 4P

To determine

The temperature on the winter day.

Answer to Problem 4P

Solution: The temperature on a winter day is $19°\text{C}$ .

Explanation of Solution

Given:

  $\begin{array}{l}T=31°\text{C}\\ t_1=4.80\text{s}\\ t_2=5.20\text{s}\end{array}$

  $v=331+0.6\times t$

At $31°\text{C}$ ,speed is $331+0.6\times 31=349.6\text{m/s}$ .

Calculations: If the echo takes 4.80s to make the return trip, the return distance is

  $d=$ $349.6\times 4.80=1678.08\text{m}$

If on a winter day,the return distance is the same $1678.08\text{m}$ and takes $5.20\text{s}$ .

  $v=\frac{1678.08}{5.20s}=322.7\text{m/s}$

  $\begin{array}{l}322.7=331+0.6\times T\\ T=19.3°\text{C}\end{array}$

Conclusion:

The temperature on a winter day is $19°\text{C}$ .