The boat moves at a speed of 18 km / h relative to the water and, keeping the course

The boat moves at a speed of 18 km / h relative to the water and, keeping the course perpendicular to the bank, crosses the river in 3 minutes 20 seconds. Determine the movement of the boat relative to the shore, if the speed of the current along the entire width of the river is 3.75 m / s.

Let the boat’s own speed relative to the water be v (s) = 18 km / h = 5 m / s. From the condition of the problem it is known that the speed of the current over the entire width of the river is v (t) = 3.75 m / s. The boat speed vector relative to the coast can be found by the vector addition rule, that is, by the parallelogram rule. Since the boat is heading perpendicular to the shore, the vectors of the boat’s own speed and the speed of the river flow are perpendicular, which means that the parallelogram built on these vectors will be a rectangle, and the module of the boat’s speed vector v (l) relative to the shore will be its diagonal. It can be found by the Pythagorean theorem: v (l) ^ 2 = v (c) ^ 2 + v (t) ^ 2 or v (l) ^ 2 = (5 m / s) ^ 2 + (3.75 m / c) ^ 2; v (l) = 25/4 = 6.25 (m / s). To determine the modulus of movement of the boat relative to the shore S according to the formula S = v (l) ∙ t, it is necessary to take into account that the boat crosses the river in time t = 3 minutes 20 s = 200 s. We get: S = 6.25 m / s ∙ 200 s = 1250 m = 1.25 km.
Answer: the movement of the boat relative to the coast is 1.25 km.