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Yahoo!

  • 2 years ago

A machine gun is mounted on the top of tower 100m high.At what angle should the gun be inclined to cover a max range of firing the ground below?Muzzle speed=150m/s,take g=10m/s^2

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  1. siddhantsharan
    • 2 years ago
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    Okay. This is going to take some time. First we find the time. |dw:1347968161543:dw|

  2. siddhantsharan
    • 2 years ago
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    Now, \[-100 = (150\sin \theta)t - 5t^2\] \[t^2 - 30\sin \theta t -20=0\] Solving for t, \[t = [30\sin \theta \pm \sqrt{(900\sin^2 \theta) + 80}]/2\]

  3. siddhantsharan
    • 2 years ago
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    Now , We need to find the expression for range. \[Range = (150\cos \theta)*t\]

  4. siddhantsharan
    • 2 years ago
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    Substituting t and maximizing your expression will give you the answer.

  5. siddhantsharan
    • 2 years ago
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    To maximize differenciate R with respect to theta.

  6. siddhantsharan
    • 2 years ago
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    @Yahoo! Calculation is there. But other than that, Do you get it?

  7. Yahoo!
    • 2 years ago
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    Yup....i understood...ur method.....Does...This...need...Serious....Calculus...Since....i am ..not very much exp with it...

  8. siddhantsharan
    • 2 years ago
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    No. Not really. You know product rule, right?

  9. siddhantsharan
    • 2 years ago
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    You should get a value close to 45 degrees. Maybe something like 43 degrees or 44.

  10. Yahoo!
    • 2 years ago
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    Yup..it shuld be 43.75

  11. siddhantsharan
    • 2 years ago
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    Yeah. :)

  12. Yahoo!
    • 2 years ago
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    thxxx

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