A motor boat floats down the river from one point to another and back. How many times

| May 25, 2021 | education

A motor boat floats down the river from one point to another and back. How many times is the time of movement of the boat against the current longer than the time of movement with the current, if the speed of the current is 2.0 m / s, and the speed of the boat in still water is 10 m / s?

Vt = 2 m / s.

V = 10 m / s.

t2 / t1 -?

The speed of the motor boat relative to the coast when moving behind the current V1 will be the sum: V1 = V + Vт.

Since the boat moves uniformly in a straight line, then the time of movement of the boat behind the current t1 is expressed by the ratio: t1 = S1 / V1 = S1 / (V + Vt).

The speed of the motor boat relative to the bank against the current V2 will be the difference: V2 = V – Vт.

The time of movement of the boat against the current t2 is expressed by the ratio: t2 = S2 / V2 = S2 / (V – Vt).

Since the boat travels the same distance, which is behind, which is against the current, then S1 = S2.

t2 / t1 = S2 * (V + Vt) / (V – Vt) * S1 = (V + Vt) / (V – Vt).

t2 / t1 = (10 m / s + 2 m / s) / (10 m / s – 2 m / s) = 1.5.

Answer: the time of movement of the boat behind the current is 1.5 times less than the time of movement of the boat against the current t2 / t1 = 1.5.



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