How to Solve for A and Theta in a Difficult Vector Problem?

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In summary: Use that to solve for \theta.In summary, the conversation discusses using the component method to determine A and Theta for a resultant R of three forces A, B, and C. A system of equations is set up to solve for A and Theta, with one equation involving only A and the other involving both A and Theta. The solution involves substituting A into the second equation and solving for Theta.
  • #1
ur5pointos2sl
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< is the angle symbol here.

R is the resultant of three forces A,B,C that is R = A+B+C
If A = A<210, B=200 < Theta, C=200 <65, and R = 250 <125, use the component method to determine A and Theta.

ok so I broke them into their components and now I have no idea how to find A and Theta

Ax = A cos 30
Ay = A sin 30
Bx = 200 cos Theta or possibly could be 200 sin Theta
By = 200 sin Theta or 200 cos Theta
Cx=200 cos 65
Cy = 200 sin 65
Rx = 250 sin 35
Ry = 250 cos 35

A cos 30 + 200 cos Theta + 200 cos 65 = 250 sin 35

A sin 30 + 200 sin Theta + 200 sin 65 = 250 cos 35

would this be the correct approach? How in the world would you solve for A or Theta?
 
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  • #2
[tex]Acos210+200cos\theta = 250cos135-200cos65[/tex]
[tex]Asin210+200sin\theta = 250sin135-200sin65[/tex]
You have two equations with two unknows, so you have a system and can find the variables.
 
Last edited:
  • #3
Jebus_Chris said:
[tex]Acos210+200cos\theta = 250cos135-200cos65[/tex]
[tex]Asin210+200sin\theta = 250sin135-200sin65[/tex]
You have two equations with two unknows, so you have a system and can find the variables.


I am not really sure how to solve the system. I haven't taken linear algebra and surely haven't dealt with any systems like this. Could someone please help
 
  • #4
Just solve for A and substitute.
 
  • #5
Solve one for A and the plug that into the other and then you can find theta.
 
  • #6
Jebus_Chris said:
Solve one for A and the plug that into the other and then you can find theta.

ok sounds simple enough..let me try and see
 
  • #7
ur5pointos2sl said:
ok sounds simple enough..let me try and see

ok maybe not so simple..I am going to have to pass on this. I cannot solve this system to save my life.

I get

A = (30.2 - 200 cos Theta)/cos 30

and

A=(23.4 - 200 sin Theta)/sin 30

not even sure if this is correct..if I plug in A then I have Cos and Sin in one equation and not sure what to do with it.:confused:
 
  • #8
You know A in terms of [tex]\theta[/tex], so take one of your values for A and place it into the other equation. Then you'll have only constants and [tex]\theta[/tex] in the resulting equation.
 

1. What is a difficult vector problem?

A difficult vector problem is a mathematical problem that involves calculating and manipulating vectors, which are quantities that have both magnitude and direction. These problems can be challenging because they require a strong understanding of vector operations, properties, and applications.

2. What types of vector problems are considered difficult?

Difficult vector problems can vary in their complexity and difficulty. Some common types include finding the resultant of multiple vectors, calculating the angle between vectors, and solving vector equations. Vector problems that involve three-dimensional space or non-linear motion can also be particularly challenging.

3. How can I approach solving a difficult vector problem?

When faced with a difficult vector problem, it is important to visualize the vectors and understand their properties. This can help in determining the appropriate vector operations to use in solving the problem. It may also be helpful to break the problem down into smaller, more manageable steps and to practice solving similar problems to build familiarity and confidence.

4. What are some common mistakes to avoid when solving a difficult vector problem?

One common mistake when solving vector problems is to confuse the magnitude and direction of a vector. It is important to pay close attention to the units and to use the correct notation for vectors. Another mistake is to forget to account for vector properties, such as the commutative and distributive properties, which can simplify calculations.

5. Are there any resources available to help with difficult vector problems?

Yes, there are many resources available to help with difficult vector problems. Online tutorials, practice problems, and textbooks can provide step-by-step explanations and examples. There are also software programs and apps that can assist with vector calculations and visualizations. Seeking help from a tutor or classmate can also be beneficial for understanding and solving difficult vector problems.

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