ï»¿ Two towns A and B are connected by a regular bus service with a bus leaving inÂ either direction every T minutes. A man cycling with a speed of 20 km h-1Â in theÂ direction A to B notices that a bus goes past him every 18 min in the direction ofÂ his motion, and every 6 min in the opposite direction. What is the period T of theÂ bus service and with what speed (assumed constant) do the buses ply on theÂ road? from Physics Motion in Straight Line Class 11 Manipur Board

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Motion in Straight Line

Physics Part I

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Two towns A and B are connected by a regular bus service with a bus leaving inÂ either direction every T minutes. A man cycling with a speed of 20 km h-1Â in theÂ direction A to B notices that a bus goes past him every 18 min in the direction ofÂ his motion, and every 6 min in the opposite direction. What is the period T of theÂ bus service and with what speed (assumed constant) do the buses ply on theÂ road?

LetÂ VÂ be the speed of the bus running between towns A and B.

Given,Â

Speed of the cyclist Â = 20 km/hrÂ

Relative speed of bus moving in the direction of the cyclist = V - v = (V-20) km/hr

Every 18 mins, the bus went past the cyclist. moving in the direction of the bus.Â

That is,Â
Distance covered by the bus =Â
One bus leaves every t minutes.Â

Therefore,Â

Distance travelled by the bus = VÂ Â  Â  Â ... (ii)Â

Equations (i) and (ii) are equal.Â

Relative speed of the bus moving in the opposite direction of the cyclistÂ = (VÂ + 20) km/h

Time taken by the bus to go past the cyclist = 6 min = 6 / 60 hÂ

Therefore,Â

Now, from equations (3) and (4), we get

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