From one point to another, the motorcyclist was driving at a speed of 60 km / h. With what speed he did

| July 10, 2021 | education

From one point to another, the motorcyclist was driving at a speed of 60 km / h. With what speed he did the opposite, if the average speed for the entire movement was 45 km / h.

V12 = 60 km / h.

Vav = 45 km / h.

S12 = S21.

V21 -?

To find the average speed of movement Vav, it is necessary to divide the entire traversed path S by the time of its passage t: Vav = S / t.

The entire path S traveled will be the sum: S = S12 + S21 = 2 * S12.

The time of movement of the body along the entire path t is expressed by the sum: t = t12 + t21.

t12 = S12 / V12.

t21 = S21 / V21.

t = S12 / V12 + S21 / V21 = (S12 * V21 + S21 * V12) / V12 * V21 = S12 * (V21 + V12) / V12 * V21.

Vav = 2 * S12 * V12 * V21 / S12 * (V21 + V12) = 2 * V12 * V21 / (V21 + V12).

Vav * (V21 + V12) = 2 * V12 * V21.

Vav * V21 + Vav * V12 = 2 * V12 * V21.

Vav * V12 = 2 * V12 * V21 – Vav * V21.

V21 = Vav * V12 / (2 * V12 – Vav).

V21 = 45 km / h * 60 km / h / (2 * 60 km / h – 45 km / h) = 36 km / h.

Answer: the motorcyclist covered the way back at a speed of V21 = 36 km / h.



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