To solve this problem we must basically resort to the kinematic equations of movement. For which speed is defined as the distance traveled in a given time. Mathematically this can be expressed as
[tex]v = \frac{d}{t}[/tex]
Where
d = Distance
t = time
For which clearing the time we will have the expression
[tex]t = \frac{d}{v}[/tex]
Since we have two 'fluids' in which the sound travels at different speeds we will have that for the rock the time elapsed to feel the explosion will be:
[tex]t = \frac{1300m}{3000m/s}[/tex]
[tex]t = 0.433s[/tex]
In the case of the atmosphere -composite of air- the average speed of sound is 343m / s, therefore it will take
[tex]t = \frac{1300m}{343m/s}[/tex]
[tex]t = 3.79s[/tex]
The total difference between the two times would be
[tex]\Delta t = 3.79s-0.433s[/tex]
[tex]\Delta t = 3.357s[/tex]
Therefore 3.357s will pass between when they feel the explosion and when they hear it
