• Support PF! Buy your school textbooks, materials and every day products Here!

Vector Component angles

  • Thread starter archa1c
  • Start date
  • #1
4
0

Homework Statement



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?

Homework Equations






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.
 

Answers and Replies

  • #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.
 
  • #3
4
0
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...
 
  • #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.
 

Related Threads on Vector Component angles

Replies
3
Views
636
Replies
3
Views
35K
Replies
2
Views
1K
Replies
8
Views
672
Replies
12
Views
26K
Replies
1
Views
2K
  • Last Post
Replies
12
Views
9K
Replies
4
Views
1K
Top