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Simple Dynamics Question

  1. Feb 18, 2008 #1
    1. The problem statement, all variables and given/known data

    A projectile is fired at an angle of 30 degrees above the horizontal with a velocity V0 of 460 m/s. Determine the radius of the curvature of the trajectory at the position of the particle 10 seconds after firing.


    2. Relevant equations

    v = u + at
    s = ut + 0.5at(squared)
    v(squared) = u (squared) + 2 as

    3. The attempt at a solution

    No idea. Im trying to do this question but i havent been taught how to work out the angles during flight. Can anyone help?
     
  2. jcsd
  3. Feb 19, 2008 #2
    Bump, i still cant work this out.
     
  4. Feb 19, 2008 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    First determine the trajectory! Of the equations you wrote
    v = u + at
    s = ut + 0.5at(squared)
    v(squared) = u (squared) + 2 as
    Only s= ut+ 0.5at2 will help and you need to convert into x and y coordinates. Of course the acceleration vector a= <0, -9.8> so the equations for x and y separately are x= ux t and y= uy- 4.9t2.

    You have an speed 460 m/s and angle 30 degrees. Do you know how to find the x and y components of velocity? Once you do that you have equations for x and y depending on the parameter t.

    "Determine the radius of the curvature of the trajectory at the position of the particle 10 seconds after firing."

    If you are expected to be able to do this, then you must have been given formulas for "curvature" and "radius of curvature". Do you know a formula for the radius of curvature of a graph in the xy plane where x and y are given as functions of a parameter?
     
  5. Feb 19, 2008 #4
    Unfortunatly i havent been given any equations for the curvature. Either im missing something, or do you think it could mean the radius of the curve is the height of the ball at that time, and take that height as the radius.

    It doesnt really make sence considering its not a circle its a parabola. Thank you for your help, do you have any idea what he could mean in the question if im not given an equation for the radius of the curvature?
     
  6. Feb 20, 2008 #5
    Bump, really need help with this.
     
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