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Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm . F ind the time when the distance between the two persons is least?

Two straight tracks AOB and COD meet each other at rt angles at point O.A person walking at a speed 5 km/hr along AOB is at crossing O at 12 o clock noon, another person with speed 5 km/hr walking along COD reaches O at 1:30 pm .


F ind the time when the distance between the two persons is least?

Grade:11

1 Answers

Saurabh Singh
askIITians Faculty 49 Points
10 years ago
at time t hours after 1:30

first person will be (7.5+5t) from O
second person will be (5t) from O

distance between two will be
(7.5+5t)^2 +(5t)^2
we need to minimize this
the plot would look like -->



179-428_MSP120920a0b008g4dh730c000035i9h49db4ih64aa.gif

so they are closest at 0.75 hours before 1:30
i.e 45 minutes before 1:30
i.e 12:45

Thanks & Regards

Saurabh Singh,

askIITians Faculty

B.Tech.

IIT Kanpur

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