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Independence of Perpendicular Components of Motion
It is often said that perpendicular components of motion are independent of each other. A horizontal motion is independent of vertical variables of motion and a vertical motion is independent of horizontal variables.
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Many physics students approach this question thinking that a change in the river speed will surely affect the time to cross the river. But don't be fooled! The two simultaneous motions that are occurring - the motion across the river and the motion down the river - are independent of each other. Crossing a river is a crossways thing; traveling downstream is a downstream thing. The only variable these two motions have in common is time; both motions occur for the same amount of time. The time to cross the river is dependent upon variables directed across the river - the river width and the boat speed in the crossways direction. The river velocity, being a downstream variable, does not affect the time to travel across the river.
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The motion of a boat across a river involves two simultaneous and independent motions - the motion perpendicular to the river banks and the motion parallel to the river banks. The motion perpendicular to the river banks is dependent upon the variables that are directed across the river - river width and boat velocity. The river velocity, being perpendicular to the crossways motion of the boat, does not affect the time to cross the river. Any alteration in the river velocity will have no effect upon the time to cross the river.
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