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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?

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?

Grade:10

1 Answers

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 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
Askiitians Faculty

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