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

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Motion in Straight Line

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

Let V be the speed of the bus running between towns A and B.

Given,

Speed of the cyclist  = 20 km/hr

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.

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

Therefore,

Distance travelled by the bus = V      ... (ii)

Equations (i) and (ii) are equal.

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

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

Therefore,

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

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