The shooter hears the sound of a bullet hitting the target 1 second after the shot. How far is the target from it?

| April 2, 2021 | education

The shooter hears the sound of a bullet hitting the target 1 second after the shot. How far is the target from it? The speed of the bullet is 500 m / s, the speed of sound is assumed to be 333 m / s.

t = 1 s.
Vpool = 500 m / s.
Vsv = 333 m / s.
S -?
The time t after which the shooter hears the sound of the bullet hitting the target after the shot will be the sum of the time of the bullet’s flight tp and the time of movement of the sound from the target with it ts: t = tp + tsv.
The time of movement of the bullet is determined by the formula: tp = S / Vpool.
The sound travel time is determined by the formula: tsv = S / Vsv.
t = S / Vpool + S / Vsv.
S = (Vpool * Vsv) * t / (Vpool + Vsv).
S = (550 m / s * 333 m / s) * 1 s / (550 m / s + 333 m / s) = 207.4 m.
Answer: the target is located at a distance of S = 207.4 m.



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