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!

Vector Component angles

  1. Oct 4, 2009 #1
    1. The problem statement, all variables and given/known data

    A velocity of [tex]10ms^{-1}[/tex] is to be replaced by two components, [tex]7.0ms^{-1}[/tex] and [tex]5.0ms^{-1}[/tex]. What must be the angle between the two components?

    2. Relevant equations




    3. The attempt at a solution

    Now I think that the answer to the solution lies in using trig to work out the angles, and that solving this equation [tex](5 sin\Theta)^2 + (7 + 5cos\Theta)^2 = 10^2[/tex] should give me the respective answers. What I don't understand is WHY I am doing that. So if someone could be so kind as to tell me how I would reach the conclusion that I should do those steps I would be very grateful.
     
  2. jcsd
  3. Oct 4, 2009 #2
    Hmm, you should use the fact that

    Vx=Vcos(theta)
    Vy=Vsin(theta) and that Vx^2+Vy^2 = V^2
    where Theta is the angle between the components. I'm not sure why you have a (7+5cos(\theta))^2 there.
     
  4. Oct 4, 2009 #3
    Well in my book I am basically told to use this equations (Where Vr is the resultant):

    [tex]V_r^2 = (V_1 sin\Theta)^2 + (V_1 cos\Theta + V_2)^2[/tex] - I want to know why I would use this forumla...
     
  5. Oct 5, 2009 #4
    Have you learned something called the cosine rule before? The cosine rule says,
    that if I have 2 vectors a and b, |a+b|^2=a^2+b^2+2abcos(theta).

    Now, relate that to the formula written in the book.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook