1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Finding Length of a Vector

  1. Aug 31, 2010 #1
    1. The problem statement, all variables and given/known data
    Find the length of the vector C starting from the components given in Equations 3 and 4.
    Express C in terms of A, B, and theta.


    2. Relevant equations
    3. Cx= A + Bcos([tex]\theta[/tex]),
    4. Cy = Bsin([tex]\theta[/tex]).


    3. The attempt at a solution
    C = [tex]\sqrt{C_x ^2+C_y ^2}[/tex]
    C = [tex]\sqrt{A^2+(Bcos\theta)^2+(Bsin\theta)^2}[/tex]
    using trig identity cos2 [tex]\theta[/tex]+sin2 [tex]\theta[/tex]=1
    C = [tex]\sqrt{A^2+2B^2}[/tex] ???
     
  2. jcsd
  3. Aug 31, 2010 #2

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    You have all the right ingredients, but be careful!

    [tex](A + B \cos\theta)^2[/tex] is not the same as [tex]A^2 + (B \cos\theta)^2[/tex].

    This is a classical trap... (x + 1)² is not equal to x² + 1²... to see what it does equal, you can write it out as (x + 1)(x + 1) and expand the brackets.
     
  4. Aug 31, 2010 #3
    C = [tex]\sqrt{A^2 + 2ABcos\theta + B^2}[/tex]
     
  5. Aug 31, 2010 #4

    CompuChip

    User Avatar
    Science Advisor
    Homework Helper

    Now you're just sloppy and maybe guessing a bit, aren't you? :)
    Please work it out carefully and you'll get the right answer.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook