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anonymous

  • 5 years ago

a ship travelling with a constant speed and direction is sighted from a lighthouse. at this time it is bearing of 042. half an hour later on a bearing of 115 at a distance of 7.6km from the same lighthouse. find its speed in km per hour

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  1. anonymous
    • 5 years ago
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    MissMysterioulsyStupid, have you given us all the information? Are you possibly missing another distance?

  2. anonymous
    • 5 years ago
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    oh sorry i missed out 2.7 its a ship travelling with a constant speed and direction is sighted from a lighthouse. at this time it is 2.7 km bearing of 042. half an hour later on a bearing of 115 at a distance of 7.6km from the same lighthouse. find its speed in km per hour

  3. anonymous
    • 5 years ago
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    Okay - now I can help you.

  4. anonymous
    • 5 years ago
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    thx

  5. anonymous
    • 5 years ago
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    You just have to use the cosine rule. Have you got a picture of what the setup is supposed to look like?

  6. anonymous
    • 5 years ago
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    no, were supposed to work it out ouselves and i dunno how to do bearings

  7. anonymous
    • 5 years ago
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    Bearings always start from due north (0 degrees) , and when you trace out an angle (e.g. 42 degrees) you do so in a clockwise direction.

  8. anonymous
    • 5 years ago
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    So, draw a small vertical line to represent your lighthouse, then put your pen flat on the page along the lighthouse and turn it about 42 degrees. Put a point somewhere after you've turned and draw a line from that point to your lighthouse.

  9. anonymous
    • 5 years ago
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    Next, all you have to do is repeat the whole angle sweeping thing with your pen again, this time for the new angle. So starting from due north, sweep about 115 degrees clockwise and mark another point. Now just draw a line from the lighthouse to that point.

  10. anonymous
    • 5 years ago
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    Finally, draw a line between your two points - this will be the path the ship has taken. Oh, I forgot to tell you to make the 115 degree line with 7.6km.

  11. anonymous
    • 5 years ago
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    ok, ive got a traingle i think its right

  12. anonymous
    • 5 years ago
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    Okay, nearly there...the angle closest to the lighthouse is going to be 115 degrees - 42 degrees (because we just want the angle that's living in the triangle). That should work out to 73 degrees. If you label the unknown distance (the distance between your points, which is the distance the ship has traveled) with something like, 'd', you have everything that's needed for the cosine rule (you can use the cosine rule in any plane triangle when you have two sides and the angle IN BETWEEN given)).

  13. anonymous
    • 5 years ago
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    I won't leave you hanging - I'll do the mathematics, but I hope everything was explained well enough for you to be able to do it yourself... \[d^2=(2.7)^2+(7.6)^2-2(2.7)(7.6)\cos(73)\approx53.05km^2\]

  14. anonymous
    • 5 years ago
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    Taking the square root of both sides gives you the distance traveled:\[d \approx 7.28km\]which sounds reasonable. The speed is just the amount of distance it covers per unit time, so\[speed=\frac{7.28km}{0.5h}=14.57km/h\]

  15. anonymous
    • 5 years ago
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    i got the d as 7.1 :S dont u do the pythagorus theorum there?

  16. anonymous
    • 5 years ago
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    No, Pythagoras' Theorem is only applicable to right-angled triangles. That's the trick - they want you to use either the sine or cosine rule to get your answer.

  17. anonymous
    • 5 years ago
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    oh ok thx

  18. anonymous
    • 5 years ago
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    No probs.

  19. anonymous
    • 5 years ago
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    ur a life saver:) *bow* *bow*

  20. anonymous
    • 5 years ago
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    Why, thank you :p

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