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beth12345

  • 2 years ago

A boy and girl both swim at 3.0m/s. They jumpinto a river 1.0km across, with a current of 2.0m/s (E). She swims straight across relative to the shore. How long (in minutes) does each take to cross the river

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  1. shubham
    • 2 years ago
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    You are given the velocity of boy and girl w.r.t the ground and velocity of current w.r.t ground. Velocity of girl w.r.t ground, V(g,G) = 3 m/s Velocity of current = V (c,G) = 2 m/s Now, velocity of girl w.r.t current = V(g,G) + V(c,G) [ vector sum!! ] Hope you may try to solve it now...

  2. beth12345
    • 2 years ago
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    is it 5m per second

  3. shubham
    • 2 years ago
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    No... I said the vector sum, as the direction of speeds are different you can't just add both the velocities..

  4. beth12345
    • 2 years ago
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    oh would I use a squared +b squared = c squared

  5. shubham
    • 2 years ago
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    Exactly....

  6. beth12345
    • 2 years ago
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    i got 3.6

  7. shubham
    • 2 years ago
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    But, think.. For calculating time she required to cross the river if she propells herself perpendicular to the shore, would in anyway be affected by velocity of current.

  8. shubham
    • 2 years ago
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    Think why time depends on both components...

  9. beth12345
    • 2 years ago
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    uhm, I don`t understand

  10. beth12345
    • 2 years ago
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    |dw:1331693378113:dw| this is all I understand so far...

  11. shubham
    • 2 years ago
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    Right. See, She propells herself perpendicular to the bank at 3 m/s and at the same time she is getting pushed sideways at 2 m/s. So, her resultant velocity will be directed at an angle b/w the two.

  12. shubham
    • 2 years ago
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    |dw:1331693676065:dw|

  13. shubham
    • 2 years ago
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    Now, see 3m/s contributes to her getting across the bank. Time she requires = 1000 m / 3 m/s = 333.33 sec.

  14. beth12345
    • 2 years ago
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    and then it makes an angle triangle like this |dw:1331693918116:dw| ?

  15. beth12345
    • 2 years ago
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    and then it is 5.6 minutesÉ

  16. beth12345
    • 2 years ago
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    minutes*

  17. shubham
    • 2 years ago
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    RIght, you may shift vectors in a plane, without changing the directions and magnitude.

  18. shubham
    • 2 years ago
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    Yes...

  19. beth12345
    • 2 years ago
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    oh i think i get it, does the 2m per s affect it?

  20. shubham
    • 2 years ago
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    No, it doesn't effect the time, but other parameters like where she would land on the other bank does.

  21. beth12345
    • 2 years ago
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    ok, is it the same for the boy then?

  22. shubham
    • 2 years ago
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    Yes, Gender doesn't effect the time as well.. lol..

  23. beth12345
    • 2 years ago
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    oh right! haha well thanks for helping :)

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