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Aadarsh

A boat which has speed of 5 km/hr in still water crosses a river of width 1 km along the shortest possible path in 15 minutes. The velocity of the river water in km/hr is : a) 4 b) 3 c) 1 d) 2

  • 2 years ago
  • 2 years ago

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  1. Mani_Jha
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    Did you solve this?

    • 2 years ago
  2. Aadarsh
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    I tried, but didn't get the equation.

    • 2 years ago
  3. Aadarsh
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    Can u say the equation?

    • 2 years ago
  4. Mani_Jha
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    Let me see what diagram you've drawn first. By the way, if x is the river's speed, the final equation will be: \[\sqrt{25-x ^{2}}*15/60=1\]

    • 2 years ago
  5. Aadarsh
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    Can I post tomorrow? I have to go now to a hospital.

    • 2 years ago
  6. Mani_Jha
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    All right! What happened by the way?

    • 2 years ago
  7. Aadarsh
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    Regular checkup, That's all.

    • 2 years ago
  8. Aadarsh
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    |dw:1333604852676:dw|

    • 2 years ago
  9. Aadarsh
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    @Mani_Jha < can u explain now?

    • 2 years ago
  10. Mani_Jha
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    @Aadarsh, the shortest possible path is that straight line marked 1 km. Now if you attempt to move in this line, the flow of the river will deflect you to a longer path. |dw:1333690533060:dw| You attempt to move through AB, but the river deflects you to the path BC, which is longer. Now try to think: What path must you take, so that, even after the deflection, you take the shortest path AB? Understood?

    • 2 years ago
  11. Mani_Jha
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    |dw:1333690831284:dw|

    • 2 years ago
  12. Aadarsh
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    So should we take AC?

    • 2 years ago
  13. Aadarsh
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    @Mani_Jha bhai, u der? Please say now what to do.

    • 2 years ago
  14. Mani_Jha
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    Sorry, I should have mentioned AC is the direction of flow of the river. You can't take AC. Whenever you attempt to move in some direction, the flow of the river deflects you by some angle. |dw:1333691551644:dw| See that if you take this path BA, the river flow will deflect you to the path AC, which is exactly what you want, since it's the shortest path. You can apply this technique while swimming in a river too. Do you understand this? I've assumed that you know vectors.

    • 2 years ago
  15. Mani_Jha
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    So, your speed is sqrt(25-x^2). distance is 1 km and time is 15 minutes. Now find x.

    • 2 years ago
  16. Aadarsh
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    Thanks bhai, got it. x = 3. Thanks a lot.

    • 2 years ago
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