Suppose you are anchored near the shore of a channel in which there is steady current, and you are going to run your (motor) boat at constant throttle to a dock directly across the channel on the oppo

Question

Suppose you are anchored near the shore of a channel in which there is steady current, and you are going to run your (motor) boat at constant throttle to a dock directly across the channel on the opposite shore. The way in which one might steer the boat to the dock is pointing method. In pointing method keep the nose of the boat pointed directly at the dock. Velocity of boat with respect to water is ' $v$ ' and velocity of water is ' $u$ '. Width of water channel is ' $b$ '. The time taken by boat to reach the dock is :-

TestHub · Accepted Answer

u t 0 ​ = v ∫ 0 t 0 ​ ​ cos α d t v − u cos α = − d t d s re l ​ ​ ∫ 0 t 0 ​ ​ ( v − u cos α ) d t = ∫ b 0 ​ − d s re l ​ v t 0 ​ − v u 2 t 0 ​ ​ = b t = v 2 − u 2 b v ​

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