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A man wishes to cross a river which is f...

A man wishes to cross a river which is flowing at a certain speed . Man uses a motor boat whose velocity with respect to water is more than speed of flow. Minimum possible time the boat takes to cross the river is `t_(1)` , but drift along the length of river is x . When boat takes shortest route to cross the river , then it takes time `t_(2)` . Find the velocity of boat with respect to water .

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AI Generated Solution

To solve the problem, we need to analyze the motion of the boat in two scenarios: crossing the river in minimum time and crossing the river in the shortest path with no drift. ### Step-by-Step Solution: **Step 1: Define Variables** - Let \( v \) be the velocity of the boat with respect to water. - Let \( u \) be the speed of the river flow. - Let \( w \) be the width of the river. ...
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