# 2 roads intersect at right angles.car a is situated at P which is 500m from the intersection O on one of the roads.car b is at Q, 400m from O on the other road.They start out at the same time and travel towards the intersection at 20m/s and 15m/s respectively.what is the minimum distance between them?

Arun Kumar IIT Delhi
8 years ago
Hello Student,

$\\at any time from start \\r_A=(500-20t)i \\r_B=(400-15t)j \\=>d^2=(500-20t)^2+(400-15t)^2 \\now differentiate is to get the minima \\make sure t you got is \leqmin({400 \over 15},{500 \over 20 })$

Thanks & Regards
Arun Kumar
Btech, IIT Delhi