What is the angle between two vector components?

In summary, the conversation discusses how to determine the angle between two components of velocity, given the total velocity and the individual components. The solution involves using trigonometry and the cosine rule to find the angle. The formula V_r^2 = (V_1 sin\Theta)^2 + (V_1 cos\Theta + V_2)^2 is used to solve for the angle.
  • #1
archa1c
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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.
 
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  • #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
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.
 

What are vector component angles?

Vector component angles refer to the angles between the components of a vector and a reference axis. These angles are used to represent the direction of a vector in a coordinate system.

How are vector component angles calculated?

The vector component angles can be calculated using trigonometric functions such as sine, cosine, and tangent. These functions use the lengths of the vector components to determine the angle.

Why are vector component angles important?

Vector component angles are important because they provide a more precise way of representing the direction of a vector. They also allow for vector addition and subtraction to be performed more easily.

Can vector component angles be negative?

Yes, vector component angles can be negative. Negative angles indicate that the vector is pointing in the opposite direction of the reference axis.

How do vector component angles relate to vector magnitude?

The vector component angles do not directly relate to vector magnitude. However, they are used in the calculation of vector magnitude by using the Pythagorean theorem.

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