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2D Kinematics Problem involving subtended angle

  1. Feb 11, 2014 #1
    1. The problem statement, all variables and given/known data

    Mortar crew is near the top of a steep hill. They have a mortar. They angle this mortar at an angle of [itex]\theta[/itex] = 65° . The crew fires a shell at a muzzle velocity of 228 ft/sec (69.5 m/s). How far down the hill does the shell strike if the hill subtends an angle of [itex]\phi[/itex] = 32° from the horizontal?

    How long will the mortar remain in the air?
    How fast will the shell be traveling when it hits the ground?

    Relevant diagram: http://imgur.com/apimguh
    2. Relevant equations

    Kinematic Equations:

    X= Xo + Voxt

    Y= Yo + Voyt - (1/2)at2

    3. The attempt at a solution

    First off, I'm not expecting to get all of my questions answered. I just need a little push.

    I'm not sure where to start off at here. The fact that there are two angles here confuses me in regards to how they work in the equations.

    I can say that Vox = 69.5cos(65) and that Voy = 69.5sin(65).

    I'm really thrown off by the way the angles work here, and whether the distance works with a simple range equation. Any tips on where to start?


    edit: Additionally, I was given the equation d = Vo + (1/2)at2 as a hint for this. Isn't this wrong though, seeing as how the velocity should be multiplied with time?
     
    Last edited: Feb 11, 2014
  2. jcsd
  3. Feb 11, 2014 #2

    Simon Bridge

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    Always start with a sketch.
    I'll start you off:

    A "mortar" in this example refers to the mortar tube or gun depending on the period.
    Think of it as a kind of cannon. Draw a dot on your page to represent the position of the mortar.

    The mortar is sitting on the side of a hill.
    The hill has a slope - given as below the horizontal.
    So draw in a (dotted) horizontal line through the mortar and figure out which way is "below" - measure the angle in that direction and draw in a bold line through the mortar indicating the slope of the hill.

    The angle of the mortar is above the horizontal - you know how to do that right?
    So draw an arrow for the initial velocity v at the correct angle.

    The mortar shell will go in a parabola until it hits the side of the hill - which keeps going down at the same angle.

    You should be able to take it from there.
     
  4. Feb 12, 2014 #3

    BvU

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    Strange that the picture seems to have been posted before Simon commented. It looks excelent.
    I checked your earlier thread and I think you only need a small nudge.

    The hint you got is suspicious, because d = Vo + (1/2)at2 is dimensionally incorrect -- as you note. Kinematic relations are OK. Look at them in a math fashion: you still have three unknowns (x, y, t) so something else is needed (for example, in flatland: y(t)=0 when poof).

    In this exercise it is the slope of the hill, that provides you with a relationship between X(t) and Y(t) at boom time. If you express it deftly in terms of d and ##\phi## you end up with only two unknowns (d and t_strike) in two equations. Bob's your uncle...
     
    Last edited: Feb 12, 2014
  5. Feb 12, 2014 #4

    Simon Bridge

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    Hmmm... looks like I didn't see it.
    Either that or it was edited in while I was doing something else.
    I don't think I took a half-hour to type the reply but I sometimes have several threads up in different tabs.

    Looking at the diagram:
    Basically the projectile ends up at a different height than it started at - this height depends on the horizontal distance traveled.

    You could think of it as the intersection of a parabola with a line - do you know how to get the gradient of a line from the slope angle?

    Once you have the (x,y) coordinates of the endpoints you can get d.

    I had a more elaborate hint but I'll reinforce BvU at this point :)
     
  6. Feb 13, 2014 #5
    It is 2D Kinematics. The time for the shell to reach horizontally at D(x) is equal to time it reaches D(y).
     
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