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The time for a boat to cross a river

작성자 Uploader : alice 작성일 Upload Date: 2019-02-17변경일 Update Date: 2019-02-26조회수 View : 312

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Calculate the time taken to cross a river with a width of L (m) and a flow velocity of Vr (m / s) using a boat with velocity Vs (m / s). No Image


Data input : L (m), Vf (m/s), Vs (m/s)




If the boat moves in the direction perpendicular to the direction of the river, the time Tmin (s) to cross the river at the shortest time is as follows. (See Figure 1)




In this case, the point B on the opposite side can not be reached and the boat arrives at the point B \\\'.

The distance D between point B and point B is as follows.




On the other hand, to cross the shortest distance, the direction of Vs should be directed upstream. (See Figure 2)

Since the velocity in the upstream direction of Vs must be equal to Vf, the boat must face the direction rotated by θ in the upstream direction.




In this case, the speed of the boat across the river is Vc = Vs * cos (θ), and the time taken to cross the river is as follows.




This can be calculated using the vector as follows.




Since T = L / Vc,




If Vf is larger than Vs, the boat can not move to the shortest distance because the boat moves downstream even if θ becomes 90 degrees.
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