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Please settle a debate about horizontal velocity

  1. Jul 19, 2007 #1
    Here's the problem:

    2 Battleships are travelling at the same speed and at the same direction. They both have the same range, i.e. they can both only fire a maximum distance which is the same for both of them.

    BB1 is in front of BB2, who is pursuing BB1.
    They are out of range.

    My opponents in the discussion think that BB1 will be able to fire backwards at a point where BB2 would have sailed into by the time the shell lands. They also think that BB2 won't be able to hit BB1 because it's moving away from it.

    I think, that out of range means out of range.
    I think that if BB2 was to sail into the path of BB1's shells, as they describe, then that means that it is in range. However that also means that BB2 will be able to hit BB1.

    I'm making the point that, if 1.6 nautical miles is the BB's range, then the shell will land 1.6 away from the ship, not 1.6 away from the point at which it was fired. I've explained to them the fact that the shell is travelling forwards slowly to begin with so won't fire as far, however the distance that it fires less by is the same distance the Battleship travels by the time the shell lands, hence it lands at its maximum range from the battleship's perspective, not from the perspective of someone viewing from an island base on Tulagi.

    One of them thinks that a bullet fired vertically upwards from a moving car will land near the point at which it was fired.

    I've tried to explain to them that if horizontally velocity is magically nullified the moment something leaves the moving object it is attached to, then jumping in the air would be suicide, however they seem to ignore everything I've written.

    The only way I can convince them I'm right is if some physics enthusiasts agree with me....provided I AM right of course!

    Thank you
  2. jcsd
  3. Jul 19, 2007 #2


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    Yes, you are correct. The principle of relativity enables you to use any inertial frame of reference in calculating the speed, but then the distance must be calculated in that frame as well. What they are doing is mixing frames of reference - calculating speed on one and distance in another.

    Taking the frame of reference of the water, if a battleship moving at 30fps fires a shell forward at a muzzle velocity of 1000fps and the flight time is 1 second, the shell will land 1030 feet from the launch point on the water. But in the frame of reference of the battleship, the shell is traveling 1000fps and therefore only travels 1000 feet from the battleship.
  4. Jul 19, 2007 #3
    Thank you. I've been trying to tell them that all along.

    I wonder if Newton ever got called a "f*****g idiot"??
  5. Jul 19, 2007 #4


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    Probably every day... in whatever equivalent expletives they used back then. :biggrin:
  6. Jul 19, 2007 #5


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    inerestingly with battleships firing North-South at 25km range you even have to take into account the coriolis forces from the rotation of the Earth.

    ps. Thats nothing to what Newton got called by Halley, Hooke and Liebnitz certainly.
  7. Jul 19, 2007 #6


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    Also nothing compared to what the Catholic Church did/tried to do to Galileo (who invented the principle of relativity as used here).
  8. Jul 19, 2007 #7
    Thanks for the replies. I copied the first reply but they're still not budging.

    I even posted a youtube video showing a baseball being shot backwards from a speeding vehicle.
    Last edited by a moderator: Sep 25, 2014
  9. Jul 19, 2007 #8


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    Apparently one of you compadres found PF as well. The way this question is asked may throw a monkey-wrench into the issue, as there is a big caveat to what we discussed above that I didn't mention:
    There are other issues that affect the targeting of guns besides simple projectile motion. The biggest one relevant here is wind. A shell fired from a ship moving at 30 kts in still wind has a 30 kt wind to deal with. So the reality is that a shell fired forward will land closer to the ship than one fired aft, as a result of that wind. And one fired to the side will land slightly astern of the ship.

    Using my example from post #2, if a ship fired a shell directly sideways in a 30fps wind and it flew for one second, it would only fall aft by a few feet (not 30 feet) due to the wind because the shell is essentially accelerating up to 30 fps sideways and one second is not enough time for it to get to 30 fps. So the longer the shot, the bigger the effect of the wind.

    Airplanes also have to deal with turning when they target their guns, and that is a non-inertial situation, so you do have to lead your target through the turn with your guns. That, of course, presents a turn rate/radius/g-force problem for pilots as your turn radius will need to be smaller than your target's if you are going to be able to pull enough lead to hit them.
  10. Jul 19, 2007 #9


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    That's a very common thought experiment used in physics classes. Nice to see an actual demonstration of it, though I would have thought with a few trials they could have matched the speed of the car and launcher a little better.
    Last edited by a moderator: Sep 25, 2014
  11. Jul 19, 2007 #10


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    All other factors being equal...

    Both ships experience an effective headwind due to their forward velocity.
    As far as everything except the hull of the ships is concerned, the ships are stationary while the wind is blowing over the bow of both ships.

    This includes the shells. They don't know the ships are moving - all they know is the relative windspeed. Thus, the rear-firing shell will have a tailwind of X knots while the forward-firing shell will have a headwind of X knots.

    The shell with the tailwind will travel farther.
    Last edited: Jul 19, 2007
  12. Jul 20, 2007 #11

    BB1 is in front of BB2, who is pursuing BB1.
    They are out of range.


    think that BB1 will be able to fire backwards at a point where BB2 would have sailed into by the time the shell lands. They also think that BB2 won't be able to hit BB1 because it's moving away from it.

    Is one or the other able to hit the other?

    my answer: no

    like yours:

    "out of range" means out of range-----

    From the parameters and the definition---that means what it means (out of range), no matter how much wind, speed, earth rotation, etc.
  13. Jul 20, 2007 #12
    So let me get this straight:

    A ship moving forwards at x fps fires a shell backwards at y fps.

    x < y

    The total velocity of the shell equals y - x.

    But how can headwind (i.e. air resistance opposing forward motion- correct?) affect a shell that's travelling in the opposite direction?

    Wouldn't everything balance out? The wind is pushing against the ship, because it's moving forwards, but that same "wind" would have no "backwards" affect on the shell because it's been fired backwards, right?

    A ship moving forwards at x fps has a "headwind" pushing against it at x fps.
    But the forces acting on the shell (in terms of its horizontal velocity) would only include the forwards motion of the ship, plus whatever air resistance it would face as it travels towards the target.

    In other words, the net force on the ship is not 0, because even though it's travelling at x fps and has the same amount pushing backwards, it's maintaining its constant speed of x fps forwards.

    Am I correct?
  14. Jul 20, 2007 #13
    Also, I forgot to mention the youtube video.
    In the video, the baseball pretty much stays at the point where it was fired (relative to the ground)- even though it has a tailwind of 100KPH?
  15. Jul 20, 2007 #14


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    A tailwind or headwind is relative to the ground, so for the baseball it is zero. For the shell, it is 1000fps plus or minus the ship speed (because the ship speed is added to or subtracted from the shell speed from the ship to get the shell's speed over ground.
  16. Jul 20, 2007 #15
    OK, so on the shell, the headwind would be 970 fps (speed of projectile fired backwards, but -30fps because that's the speed of the ship sailing forwards).

    So would that be 970 fps pushing forwards (as in, the direction of the ship), against 970 fps pushing backwards (the shell itself)?

    And conversely, would the shell fired from the ship which is pursuing the other ship, have 1030 fps pushing against the shell, but 1030 fps pushing the shell?
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