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 distance 1_(1)"and"1_(2)from O, respectively. Find the eime , when they are nearest and also the shortest distance between them .

Two particles A and B move with constant velocities v_(1)"and " v_(2)a

1.	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 distance 1_(1)"and"1_(2)from O, respectively. Find the eime , when they are nearest and also the shortest distance between them .
Answer» SOLUTION :After time .t. , the position of the point A and B are`(1_91)-v_(1)t)"and"(1_(2)-v_(2)t), `RESPECTIVELY The distance L between the POINTS A.andB. are `L_(2)=(1_(1)-v_(1)t)^(2)+(1_(2)-v_(2)t)^(2)` Differentiating with restect to time, `2L(dL)/(dt)=2(1_(1)-v_(1)t)(-v_(1))+2(1_(2)-v_(2)t)(-v_(2))` From MINIMUM value of `L(dL)/(dt)=0` PUTTING the value of t in equation (1) `L_(min)=\|1_(1)v_(2__)+1_(2)v_(1)\|/sqrt(v_(1)^(2)+v_(2)^(2))`