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# in the problem. when the distance between two approaching bodies perpendicular to each other...we need to find the minimum distance between them. how to solve it on the basis of relative velocity? take the ques. as two bodies approaching origin perpendicularly one with vel V at a distance L from origin and other vel 2V at a distance 2L from origin. please say the concept.

Prasenjit Dubey
17 Points
8 years ago

Apply maxima-minima rule

SOURAV MISHRA
37 Points
8 years ago

USING THE CONCEPT OF RELATIVE VELOCITY IS ADVANTAGEOUS OVER THE USUAL METHOD WHICH REQUIRES PYTHAGORAS THEOREM AND CALCULUS.

USING RELATIVE VELOCITY WILL REQUIRE ONLY SIMPLE GEOMETRY AND YOU CAN ALSO FIND THE TIME AT WHICH THEY APPROACH EACH OTHER IN THE MINIMUN DISTANCE.

YOU JUST HAVE TO ASSUME ONE OF THE BODIES AS FIXED AND THEN SEE THE PATH OF THE OTHER BODY. IT WILL ALWAYS BE ALONG THE RELATIVE VELOCITY OF THE 2ND BODY WITH RESPECT TO THE FIXED BODY. SINCE IN THE GIVEN SITUATION THE INDIVIDUAL VELOCITIES ARE CONSTANT AND DO NOT CHANGE WITH TIME THE PATH SEEN BY THE BODY WHICH IS ASSUMED TO BE FIXED WILL BE A STRAIGHT LINE. THE NEXT STEP IS JUST TO FIND THE PERPENDICULAR DISTANCE BETWEEN THE STRAIGHT LINE PATH AND THE BODY WHICH IS ASSUMED TO BE FIXED AT ITS POSITION.