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Bullet trajectory: Aiming a gun

  1. Jun 28, 2017 #1
    1. The problem statement, all variables and given/known data:
    A person aims a gun at a bird from a point at a horizontal distance of 100m. If the gun can impart a speed of 500m/s to the bullet , then above what height of the bird he should aim his gun to hit it ?

    2. Relevant equations:
    [itex]H_{max}=\frac{u^2\sin^2\theta}{2g}[/itex]
    [itex]R=\frac{u^2\sin2\theta}{g}[/itex]
    3. The attempt at a solution:

    Range= [itex]R=\frac{u^2\sin2\theta}{g}[/itex]


    [itex]\implies \sin2\theta=\frac{Rg}{u^2}[/itex]


    [itex]\implies \sin2\theta=\frac{1}{250}[/itex]


    [itex]\implies 2\theta=\sin^{-1}(\frac{1}{250})[/itex]


    [itex]\implies \theta\approx 0.11[/itex]


    Maximum height=[itex]H=\frac{u^2sin^2\theta}{2g}[/itex]


    [itex]\implies H=0.04 m [/itex]


    The correct answer is 20 m. Where have i gone wrong?
     
    Last edited: Jun 28, 2017
  2. jcsd
  3. Jun 28, 2017 #2

    haruspex

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    That is not the same as the max height reached. Draw a diagram.
     
  4. Jun 28, 2017 #3
    @haruspex, Here is the diagram i drew while solving this problem,
    upload_2017-6-28_15-17-39.png
     
  5. Jun 28, 2017 #4

    haruspex

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    Ok, so show on it the point above the bird that the person aims at.
     
  6. Jun 28, 2017 #5
    @haruspex, here it is:
    upload_2017-6-28_15-34-47.png
     
  7. Jun 28, 2017 #6

    haruspex

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  8. Jun 28, 2017 #7
  9. Jun 28, 2017 #8

    haruspex

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    If you point a gun in a certain direction, in what direction do you expect the bullet to emerge from the muzzle? What direction is that in your diagram?
     
  10. Jun 28, 2017 #9
    The direction of [itex]\vec{U}[/itex]?
     
  11. Jun 28, 2017 #10

    haruspex

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    Yes. So P is a point in that line and vertically above the bird.
     
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