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Two particles A and B move with constant velocities v_(1) and v_(2) along two mutually perpendicular straight lines towards the intersection point O.At moment t=0,the particle were located at distancce l_(1) and l_(2) from O. respectively .Find the time,when they are nearest and also the shortest distance between them. |
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Answer» Solution :After time .t. ,the position of the POINT A and B are `(l_(1)-v_(1)t)` and `(l_(2)-v_(2)t)`. Repectively. The distance L.between the points A. and B. are `L_(2)=(l_(1)-v_(1)t)^(2)+(l_(2)-v_(2)t)^(2)` From minimum value of `L(dL)/(dt)=0` `(v_(1)^(2)+v_(2)^(2))t=l_(1)v_(1)+l_(2)v_(2)` or `t=(l_(1)v_(1)+l_(2)v_(2))/(v_(1)^(2)+v_(2)^(2))` PUTTING the value of t in equation (1) `L_(min)=(|1_(1)v_(2)+l_(2)v_(1)|)/(sqrt(v_(1)^(2)+v_(2)^(2)))` 
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