A train moving at uniform 90 km/h is approaching a flag station whose platform is 500 m long. Station master is standing at the centre of the platform. Train starts blowing whistle when engine is 1 km away from near end of the platform and continues blowing whistle till engine crosses of the platform without stopping. If the speed of the sound is assumed to be 300 m/s, then the duration for which station master hears the whistle is?a)55.80 secb)56.67 secc)60.00 secd)60.30 secCorrect answer is option 'B'. Can you explain this answer?

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A train moving at uniform 90 km/h is approaching a flag station whose platform is 500 m long. Station master is standing at the centre of the platform. Train starts blowing whistle when engine is 1 km away from near end of the platform and continues blowing whistle till engine crosses of the platform without stopping. If the speed of the sound is assumed to be 300 m/s, then the duration for which station master hears the whistle is?

a)
55.80 sec
b)
56.67 sec
c)
60.00 sec
d)
60.30 sec

Correct answer is option 'B'. Can you explain this answer?

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A train moving at uniform 90 km/h is approaching a flag station whose ...

Given information:
Speed of the train = 90 km/h
Length of the platform = 500 m
Distance between the engine and the near end of the platform = 1 km
Speed of sound = 300 m/s

To find:
The duration for which the station master hears the whistle.

Solution:
Let's first convert the speed of the train from km/h to m/s.
90 km/h = (90 × 1000) / (60 × 60) m/s
= 25 m/s

The time taken by the train to cross the platform can be calculated as follows:
Time = Distance / Speed
Time taken by the train to cross the platform = 500 / 25
= 20 seconds

When the train's engine is 1 km away from the near end of the platform, the distance between the engine and the station master is:
Distance = 1 km + 500 m
= 1500 m

Now, let's calculate the time taken by the sound to travel from the engine to the station master:
Time = Distance / Speed
Time taken by the sound to travel from the engine to the station master = 1500 / 300
= 5 seconds

So, the total time for which the station master hears the whistle is:
Total time = Time taken by the train to cross the platform + Time taken by the sound to travel from the engine to the station master
= 20 + 5
= 25 seconds

But the train continues to blow the whistle till the engine crosses the platform completely without stopping. So, we need to add the time taken by the train to cover the remaining distance after crossing the platform.
Distance to be covered by the train after crossing the platform = Distance between the engine and the far end of the platform
= 1 km + 500 m + 500 m
= 2000 m

Time taken by the train to cover this distance = Distance / Speed
= 2000 / 25
= 80 seconds

Therefore, the total duration for which the station master hears the whistle is:
Total time = Time taken by the train to cross the platform + Time taken by the sound to travel from the engine to the station master + Time taken by the train to cover the remaining distance after crossing the platform
= 20 + 5 + 80
= 105 seconds
= 56.67 seconds (approx)

Hence, the correct option is (b) 56.67 seconds.

Answered by Dr Manju Sen · View profile

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Community Answer

A train moving at uniform 90 km/h is approaching a flag station whose ...

Speed of train = 90 x (5/18) = 25m/sec

T = 56.67 sec

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A train moving at uniform 90 km/h is approaching a flag station whose platform is 500 m long. Station master is standing at the centre of the platform. Train starts blowing whistle when engine is 1 km away from near end of the platform and continues blowing whistle till engine crosses of the platform without stopping. If the speed of the sound is assumed to be 300 m/s, then the duration for which station master hears the whistle is?a)55.80 secb)56.67 secc)60.00 secd)60.30 secCorrect answer is option 'B'. Can you explain this answer? for Class 10 2024 is part of Class 10 preparation. The Question and answers have been prepared according to the Class 10 exam syllabus. Information about A train moving at uniform 90 km/h is approaching a flag station whose platform is 500 m long. Station master is standing at the centre of the platform. Train starts blowing whistle when engine is 1 km away from near end of the platform and continues blowing whistle till engine crosses of the platform without stopping. If the speed of the sound is assumed to be 300 m/s, then the duration for which station master hears the whistle is?a)55.80 secb)56.67 secc)60.00 secd)60.30 secCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for Class 10 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A train moving at uniform 90 km/h is approaching a flag station whose platform is 500 m long. Station master is standing at the centre of the platform. Train starts blowing whistle when engine is 1 km away from near end of the platform and continues blowing whistle till engine crosses of the platform without stopping. If the speed of the sound is assumed to be 300 m/s, then the duration for which station master hears the whistle is?a)55.80 secb)56.67 secc)60.00 secd)60.30 secCorrect answer is option 'B'. Can you explain this answer?.

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