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Motion in Straight Line

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Physics Part I

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Physics

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CBSE Gujarat Board Haryana Board

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Class 10 Class 12
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, 18 over 60 space h r s
Distance covered by the bus = left parenthesis straight V minus 20 right parenthesis cross times 18 over 60 space km space space space space space space space... space left parenthesis straight i right parenthesis space
One bus leaves every t minutes. 

Therefore, 

Distance travelled by the bus = V cross times space straight T over 60     ... (ii) 

Equations (i) and (ii) are equal. 

left parenthesis straight V space minus space 20 right parenthesis space cross times space fraction numerator 18 space over denominator space 60 end fraction space equals space fraction numerator VT space over denominator 60 end fraction space space space space space space space space... left parenthesis iii right parenthesis

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, 

left parenthesis straight V plus 20 right parenthesis space cross times space 6 over 60 space equals space VT over 60 space space space space space space... space left parenthesis iv right parenthesis

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

space space space space space space space space space space left parenthesis straight V space plus space 20 right parenthesis space cross times space 6 space divided by space 60 space equals space left parenthesis straight V space minus space 20 right parenthesis space cross times space 18 space divided by space 60

space rightwards double arrow space space space space space space space space space straight V space plus space 20 space equals space 3 straight V space minus space 60 space

rightwards double arrow space space space space 2 straight V space equals space 80 space straight V space equals space 40 space km divided by straight h
Putting space the space value space of space straight V space in space equation space left parenthesis iv right parenthesis comma space we space get space

left parenthesis 40 space plus space 20 right parenthesis space cross times space 6 space divided by space 60 space equals space 40 straight T space divided by space 60

space space space space space space space space space space space straight T space equals space 360 space divided by space 40 space equals space 9 space min


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