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### Motion in a straight line NCERT Solutions Class 11 Physics - Solved Exercise Question 3.9

Question 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?

Solution:

Let V be the speed of the bus running between towns A and B.
Speed of the cyclist, v = 20 km/h
Relative speed of the bus moving in the direction of the cyclist
= Vv = (V – 20) km/h
The bus went past the cyclist every 18 min i.e., 18 / 60 h (when he moves in the direction of the bus).
Distance covered by the bus = (V - 20) X 18 / 60 km    .... (i)
Since one bus leaves after every T minutes, the distance travelled by the bus will be equal to
V X T / 60    ....(ii)
Both equations (i) and (ii) are equal.
(V - 20) X 18 / 60 = VT / 60     ......(iii)
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

(V + 20) X 6 / 60 = VT / 60    ....(iv)
From equations (iii) and (iv), we get
(V + 20) X 6 / 60 = (V - 20) X 18 / 60
V + 20 = 3V - 60
2V = 80
V = 40 km/h
Substituting the value of V in equation (iv), we get
(40 + 20) X 6 / 60 = 40T / 60
T = 360 / 40 = 9 min