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Contact for Online Tutoring in Physics, Math, Chemistry, English ... Solutions/ Answers to NCERT/CBSE PHYSICS Class 11(Class XI)textbook. Exercise and ...
NCERT/CBSE PHYSICS CLASS 11 textbook http://www.TutorBreeze.com Contact for Online Tutoring in Physics, Math, Chemistry, English Solutions/Answers to NCERT/CBSE PHYSICS Class 11(Class XI)textbook Exercise and Additional exercise CHAPTER THREE MOTION IN A STRAIGHT LINE EXERCISES 3.9 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?

Q. 3.9 Let the speed of each bus = VB km/hr speed of cyclist = VC = 20 km/hr (1)

Let us first consider that the bus is moving in the direction of motion of cyclist from A to B.So

Vb − Vc = ( Vb − 20 ) km / h

As the bus goes past the cyclist every 18 minutes, distance covered by the bus w.r.t. 18 cyclist = ( Vb − 20 ) × km − − (1) 60 Since the bus leaves after every T minutes, so the distance covered vt the bus in T I  T  min =  h  = Vb × − ( 2) 60  60  From (1) and (2) we get ⇒ Vb − 20 = Vb ×

Now (2)

T − 18

(3)

Let, Bus moving in the direction opposite to the motion of the cyclist.

So relative speed of the bus coming from town B to A w.r.t. cyclist

= ( Vb + 20 ) km/ hr Since the bus goes past the cycle every 6 minutes. Distance covered by the bus w.r.t. the cyclist = ( Vb + 20 ) × ©TutorBreeze.com Please do not copy the answer given here Write to us for help in understanding the solution

6 km 60

( 4)

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Also the distance covered by the bus in T minutes is = ( Vb × ) × Equating (4) and (5), we get 6 T = Vb × 60 60 T Vb + 20 = Vb × (6) 6

( Vb

+ 20 ) ×

Dividing (6) and (3), we get Vb + 20 =3 Vb − 20 Vb + 20 = 3Vb − 60 2Vb = 80 Vb = 40

km / h

putting the value of Vb in equation (3), we get 40 − 20 = 40 ×

T 18

T = 9 minutes Vb = 40 km/h,

T = 9 min

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T km 60

(5)