Q26 of 35 Page 55

Two particles a and b move with velocities v1 and v2 respectively along the x and y-axis. The initial separation between them is d. Find the least distance between them during their motion.

a moves in x-direction with a velocity and b moves in y direction with velocity.

At time = t = 0


Let ‘a’ be at () and ‘b’ be at (). Also distance between them at t = 0 is d.


At t = 0,



Now, using Pythagoras theorem, we get:



Now, at any time t,


Let a be at () and b be at ()


Now, we know that,



Or,


So, using the above relation:




Now, distance between a and b at time t =


Now, is given by:






Now, for finding maxima and mminima, e always differentiate and equate the derivative to zero.




Now, putting this value of t in, we get:





Hence the least distance between them is.


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