Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of - Physics MCQ Physics | ExamTest.live | ExamTest.live

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Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

A $9 min, 40 km/h$
B $25 min, 100 km/h$
C $10 min, 90 km/h$
D $15 min, 120 km/h$

Solution & Step-by-step Explanation

Let V_{b} be the speed of the bus and V_{g} = 60 km/h be the speed of the girl.The distance between consecutive buses is d = V_{b} \cdot T .In direction of motion, relative speed is V_{b} - V_{g} : t_{1} = \frac{d}{V _{b} - V _{g}} ⟹ 30 = \frac{V _{b} T}{V _{b} - 60} In opposite direction, relative speed is V_{b} + V_{g} : t_{2} = \frac{d}{V _{b} + V _{g}} ⟹ 10 = \frac{V _{b} T}{V _{b} + 60} Dividing the two equations: 3 = \frac{V _{b} + 60}{V _{b} - 60} ⟹ 3 V_{b} - 180 = V_{b} + 60 ⟹ 2 V_{b} = 240 ⟹ V_{b} = 120 km/h .Substituting V_{b} back: 10 = \frac{120 \times T}{120 + 60} = \frac{120 T}{180} = \frac{2}{3} T ⟹ T = \frac{30}{2} = 15 min .

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Two cities X and Y are connected by a regular bus service with a bus leaving in either direction every T min. A girl is driving scooty with a speed of 60 km/h in the direction X to Y notices that a bus goes past her every 30 minutes in the direction of her motion, and every 10 minutes in the opposite direction. Choose the correct option for the period T of the bus service and the speed (assumed constant) of the buses.

A

9 min, 40 km/h

B

25 min, 100 km/h

C

10 min, 90 km/h

D

15 min, 120 km/h

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Kinematics Relative Motion Bus Problem

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