# A motorcyclist moving along a horizontal section of the road saw that a man standing by the road hit the rail

A motorcyclist moving along a horizontal section of the road saw that a man standing by the road hit the rail, and after 2 seconds he heard a sound. Determine the speed of the motorcyclist if he drove past the person 36 seconds after the impact.

t = 2 s.

T = 36 s.

Vsv = 340 m / s.

Vm -?

From hitting the rail until the moment the motorcyclist heard the sound, he traveled the distance S1 = Vm * t.

The sound from the moment of hitting the rail and meeting the motorcyclist traveled the distance S2 = Vsv * t, where Vsv is the speed of sound, which we will consider Vsv = 340 m / s.

The distance S that the motorcyclist traveled from the moment of impact to the place of impact can be expressed by the formula: S = Vm * T.

S = S1 + S2.

Vm * T = Vm * t + Vsv * t.

Vm * T – Vm * t = Vs * t.

Vm = Vsv * t / (T – t).

Vm = 340 m / s * 2 s / (36 s – 2 s) = 20 m / s.

Answer: the motorcyclist was moving at a speed Vm = 20 m / s.

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