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Ships traveling parallel , at what angle must one ship have gun aimed to hit the othe

  1. Mar 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Two ships are traveling parallel to each other in opposite directions with seed v1 and v2. One ship fire on the other. At what angle should the gun be aimed at the target ship in order to make a hit if the shot is fired at the instant when both vessels are on the straight line perpendicular to their course? The shell velocity v0 is assumed constant.


    2. Relevant equations



    3. The attempt at a solution
    The answer in text is : theta = arccos( (v1 +v2)/v0)

    The book doesn't have an explanation, and I am having trouble just being able to draw the situation. I don't understand what it means when the problem says " when both vessels are on the strait line perpendicular to their course."
     
  2. jcsd
  3. Mar 26, 2012 #2

    gneill

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    The ships are traveling along straight paths. The paths are separated by some distance, thus they are traveling on parallel courses. At some instant in time they will be directly opposite each other, so that a line perpendicular to their paths can be drawn between them.

    attachment.php?attachmentid=45542&stc=1&d=1332785619.gif
     

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  4. Mar 26, 2012 #3

    gulfcoastfella

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Start by establishing your axes. For example, let the origin be located at one of the ships when it's path is perpendicular to the line of sight to the other ship, as given in the problem. Next, specify the x- and y-axes to be in the plane of the ocean, and the z-axis to be vertically pointed to the sky. Now specify the accelerations for each component and integrate from there.
     
  5. Mar 27, 2012 #4
    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Thank you both for your replies here is the diagram I have drawn:

    http://i42.tinypic.com/2lnzbxw.jpg

    I am still having trouble understanding with the idea of finding the angle if this is a problem involving 3-dimensions. Because the cannon can be adjusted in the x and z direction. The question may seem silly to ask here, but I am studying mechanics on my own so I don't have teacher/tutor I can ask at my convenience so thank you for your replies.
     
  6. Mar 27, 2012 #5

    gulfcoastfella

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Are you expected to account for both the elevation angle and the horizontal angle?
     
  7. Mar 27, 2012 #6

    tms

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Since the problem statement says the shell velocity is constant, either there is no gravity (in which case there is no need to elevate), or only the horizontal velocity matters (no air?).
     
  8. Mar 27, 2012 #7

    tms

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    All speeds are given as constant, so there are no accelerations. The problem is simply to find out where the target will be when the shell gets there.
     
  9. Mar 27, 2012 #8

    tms

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Draw a diagram using the firing ship's frame of reference. The answer should jump out at you.
     
  10. Mar 28, 2012 #9
    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    @tms
    thank you. I took your advise and drew the diagram and defined the velocities of the shell and boat to relative to boat one:
    http://i43.tinypic.com/2u4q1ol.jpg

    Then I solved for theta using the fact that the distance between the two boats when they are on the initial line can be represented in two ways. But the problem is when i solved for theta :http://i39.tinypic.com/dwumip.jpg
    I did not get the correct answer. I know my algebra was correct so can you tell me if the way I defined the velocities was incorrect?
     
  11. Mar 28, 2012 #10
    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    If you cannot read the images I defined velocites like this:

    Velocity(shell relative to boat one) = V(0) +V(1)
    Velocity(boat two relative to boat one) = V(2) + (V1)

    And from the given equations in the problem
    V(0)= shell velocity relative to earth,
    V(1) = velocity of boat 1 relative to earth
    V(2) = velocity of boat 2 relative to earth
     
  12. Mar 29, 2012 #11

    tms

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    The question isn't entirely clear about this, but the shell's given velocity is relative to the gun. Assuming the correct answer you quoted is correct, that is.

    Correct.

    As I said, if you do everything in that boat's frame of reference the answer jumps out at you.
     
  13. Mar 29, 2012 #12
    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Ok so instead of finding two ways to represent the initial distance of boat two from boat 1(the origin) I used boat 1 as the fram of reference but I still ended up getting
    theta = arcsin( (v1 + v2)/v0)

    Here is my diagram : http://i44.tinypic.com/ndk0fa.jpg
     
  14. Mar 29, 2012 #13

    tms

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    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    The angle of bearing is usually measured from the bow, not the beam.
     
  15. Mar 29, 2012 #14
    Re: Ships traveling parallel , at what angle must one ship have gun aimed to hit the

    Thank you for telling me that. Now I understand the problem!
     
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