# The shooter hears the sound of a bullet hitting the target 1 s after the shot.

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

t = 1 s
Vp = 500 m / s
Vz = 340 m / s
S-?
In time t = 1 s, the bullet flies to the target the distance S with a speed of Vp = 500 m / s and the sound from the impact flies the distance S from the target to the person with a speed of Vs = 340 m / s t = tp + ts. tp = S / Vp is the time of flight of the bullet to the target, tz = S / Vz is the time of flight of the sound from the target to the person. t = S / Vp + S / Vz; bring to a common denominator t = (S * Vz + S * Vp) / Vz * Vp; t = S * (Vz + Vp) / Vz * Vp; S = Vz * Vp * t / (Vz + Vp); S = 340m / s * 500m / s * 1s / 840 m / s = 202m.
Answer: the distance to the target is S = 202 m.

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