Find the magniture of the vector using the figure below

[Mdhiggenz]

Homework Statement

Find the magnitude of the vector that is the sum of the three vectors , , and in the figure : figure is the link
http://imageshack.us/photo/my-images/14/yf0134.jpg/

Homework Equations

The Attempt at a Solution

What I did was obtain A_x=0 B_x=7.5

A_y=-8.00 and B₁₃

My problem came when trying to get C_x and C_y.

The way the vector is placed in the figure confuses me but I got C_y= 12sin(25)= -10.87 since it is on the negative side, and C_x= 12Cos25=-5.07.

I then got the squareroot of A_x+B_x+C_x^2+A_y+B_y+C_y^2
Did I create the triangle wrong? If so how can I make sure to not make this same mistake

 

[Simon Bridge]

That looks OK to me...
Haven't you got Cx and Cy the wrong way around though?
After all C is longer in x than it is in y and you have Cy as the bigger.

just a niggle, Cx is not 12Cos25
... you should have written Cx = -12Cos25 because that is what it is.
(you can lose marks that way)

You are used to the angle measured wrt the x-axis ... in which case Cx=12Cos(205), which is the same.

 

[Mdhiggenz]

Thank you!

 

[Simon Bridge]

No worries - you see all the other angles were wrt the y axis? so that angle in C was 115 degrees anticlockwise from the y axis. Then you can use the same formula you used for the others.

You can always construct the kinds of angles that make the math easier for you.

 

[asteriatic]

next time.



To find the magnitude of the vector, we need to use the Pythagorean theorem which states that the square of the magnitude of a vector is equal to the sum of the squares of its components. In this case, we have to consider all three vectors: A, B, and C.

Using the given figure, we can see that the components of vector C are Cx = -5.07 and Cy = -10.87. We can also see that the components of vector A and B are Ax = 0, Ay = -8 and Bx = 7.5, By = 3.

To find the magnitude of the vector, we can use the following formula:

|C| = √(Cx² + Cy²)

Substituting the values, we get:

|C| = √((-5.07)² + (-10.87)²) = √(25.7049 + 118.1569) = √143.8618 = 11.99

Therefore, the magnitude of the vector C is approximately 11.99 units.

It is important to note that the components of vector C should be negative since they are pointing in the opposite direction of the positive x and y axes. Also, make sure to use the correct formula for finding the magnitude and double check your calculations to avoid mistakes.