A man wants to reach point B on the opposite bank of a river flowing at a speed. What minimum speed relative to water should the man have so that he can reach point B. In which direction should he swim?


Correct option is


Let v be the speed of boatman in still water.

Resultant of v and u should be along AB. Components of  along x and y direction are.



v is minimum at






A train is moving eastwards with a velocity of 10 m/sec. On a parallel track another train passes with a velocity 15 m/sec eastwards. To the passengers in the second train the first train appears to be moving with a velocity.


A man can swim at a speed of 3 km/hr in still water. He wants to cross a 500 m wide river flowing at 2 km/hr. He keeps himself always at angle of 120o with the river flow when swimming find the time he takes to cross the river.


A train is moving southwards at a speed of 30 ms–1. A monkey is running northwards on the roof of the train with a speed of 5ms–1. What is the velocity of the monkey as obserced by a person standing on the ground?