What is the angle between two vector components?

AI Thread Summary
To find the angle between two vector components of a velocity of 10 m/s represented by 7.0 m/s and 5.0 m/s, the discussion emphasizes using trigonometric relationships. The equation (5 sin(Θ))^2 + (7 + 5cos(Θ))^2 = 10^2 is derived from the Pythagorean theorem and the cosine rule. Participants clarify the reasoning behind using this equation, linking it to the cosine rule which relates the magnitudes of the vectors and the angle between them. Understanding these relationships is crucial for solving the problem accurately. The discussion ultimately focuses on applying these mathematical principles to determine the required angle.
archa1c
Messages
4
Reaction score
0

Homework Statement



A velocity of 10ms^{-1} is to be replaced by two components, 7.0ms^{-1} and 5.0ms^{-1}. 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 (5 sin\Theta)^2 + (7 + 5cos\Theta)^2 = 10^2 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.
 
Physics news on Phys.org
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.
 
Well in my book I am basically told to use this equations (Where Vr is the resultant):

V_r^2 = (V_1 sin\Theta)^2 + (V_1 cos\Theta + V_2)^2 - I want to know why I would use this forumla...
 
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.
 
Thread 'Voltmeter readings for this circuit with switches'
TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
Thread 'Correct statement about a reservoir with an outlet pipe'
The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
Back
Top