Question

Question: A column of soldiers, marching at 120paces per minute, keep in step with the beat of drummer at the head of the column. The soldiers in the rear end of the column are striding forward with the left foot when the drummer is advancing with the right foot. What is the approximate length of the column?

Short answer

Answer

The length of the column is $1.7\times {\text{10}}^{\text{2}}\text{m}$.

Step-by-step solution

Given data

A column of soldiers marching at 120 pacesper minute

Determining the concept 

First, calculate the time tin seconds, and then, by using the speed vof sound, find the approximate length lof the column.

The expression for the length of the column is given by,

l = v t

Here, l is thelength of the column, t is time and v is velocity.

Determining the approximate length of the column

The time it takes for a soldier in the rear end of the column to switch from the left to the right foot to stride forward is,

$$\begin{gathered} t=\frac{1}{120}\text{min}\times 60 \\ =0.\text{50s} \end{gathered}$$

This is also the time for the sound of the music to reach from the musician to the rear end of the column. Thus, the length of the column is given by,

I = vt

Substitute for and for into the above equation,

$$\begin{gathered} l=343\times 0.50 \\ =1.7\times {\text{10}}^{\text{2}}\text{m} \end{gathered}$$

Hence, the length of the column is $1.7\times {\text{10}}^{\text{2}}\text{m}$.