Question

A sound of the gunfire was bread in 3 second at a place 1029 m distance towards which the wind was blowing and in 5 seconds at a place 1585m distance . from which the wind was blowing find the velocity of sound and the rate at which wind was blowing ?

Answer 1

Step 1:Assigning the variables

To represent the unknow quantities by two variables

The velocity of the sound of a gunfire be x m/s and the velocity of the wind blowing is y m/s

Step 2: Using distance formula

$$\begin{gathered} speed=\frac{dis\tan ce}{speed} \\ time=\frac{dis\tan ce}{speed} \end{gathered}$$

The velocity of the sound of the gunfire travelled with the wind is (x +y) km/s

The velocity of the sound of the gunfire travelled against the wind is (x - y )m/s

Step 3 : Applying the conditions

According to the question

The time taken to travel , the sound of the gunfire with the wind

$\begin{array}{rcl}\frac{1585}{(x-y)}& =& 5\\ 1585& =& 5x-5y\\ 5x-5y& =& 1585\to 1\\ & & \end{array}$

The time taken to travel , the sound of the gunfire against the wind ,

i.e.

$$\begin{gathered} \frac{1029}{(x+y)}=3 \\ 1029=3x+3y \\ \Rightarrow 3x+3y=1029\to 2 \\ Divideequation1by5andequation2by3 \\ \Rightarrow x-y=317\to 3 \\ x+y=343\to 4 \end{gathered}$$

Step 4 : elimination method

using elimination method

adding equation 3 and 4 we get

$$\begin{gathered} 2x=660 \\ x=\frac{660}{2}=330 \end{gathered}$$

Step 5 : Substituting values

Substitute the value of x = 330 in equation 3 , we get .

$$\begin{gathered} 330-y=317 \\ -y=-13 \\ y=13 \end{gathered}$$

Hence the velocity of the sound of a gunfire 330m/s and the velocity of the wind blowing is 13 m/s