Two cars A and B are moving due east and due north at 60 km.p.h respetively. At noon A is west of B at a distance 40 km . When are the cars nearest to each other and what is the distance between them then ?

Explanation

`AD_(1)` represents the reversed velocity of B.`AB_(1)` represents the velocity of A.AE represents the resultant of the two velocities which is the relative velocity of A with respect to B. The minimum distance between the two cars is BN. BN is perpendicular to AN.
The relative speed of `A = sqrt(60^(@)+80^(2))= 100 `km.p.h
Let angle `BAN = theta` . Let the two cars be nearest to each other after a time t .
`t = (AN)/("Relative speed ") = (AB cos theta )/100 = 40/100 xx 60/100 = 6/25 s `
The minimum distance between the two cars is BN.

`BN = AB sin theta = 40 xx 80/100 = 32 km`