Component vectors positive or negative and angles positive or negative

In summary, the conversation discusses the calculation of a cruise ship's displacement vector and its magnitude and direction. The process involves breaking down the vectors into components and using the Pythagorean theorem to find the resultant vector. The direction is determined by using the inverse tangent function. The conversation also touches on the use of positive and negative angles and vectors, as well as the importance of accurately defining directions, such as east and west. Finally, the conversation mentions the relationship between physics and engineering.
  • #1
Who,me?

Homework Statement



A cruise ship leaving port, travels 50.0 km 45.0 degrees north of west and then 70.0 km 30 degrees north of east. Find
a. The ship's displacement vector (the answer is Rx=25.3 km, Ry=70.4)
b. The displacement vector's magnitude and direction (the answer is 74.8 km 70.2 degrees north of east)

Homework Equations


SOH CAH TOA in these forms
Component vectors (x and y)
X cos(angle)
X sin (angle)
Then Pythagorean equation
asquared+bsquared=csquared


The Attempt at a Solution



Here's what I am doing;
I draw a coordinate plane, my first vector is drawn 45 degrees north from the x plane, I then draw the vector going 50 km north of west into the 2nd quadrant. From that point I draw a straight line directly right as a reference point for east. I draw a 30 angle from that straight line and begin drawing the 70 km vector.
Now,
Here's what I need; the displacement vector is a straight line from my starting point directly to my finishing point. However, since it is not a right triangle I will need to find x and y component vectors for both my first vector (50km) and my second vector (70km). After that I will need to add up both x component vectors and then separately add up both y component vectors. These new components are my Rx and Ry i.e. my x and y components of my displacement vector. I take Rx squared plus Ry squared and then find the square root of that. This should be my displacement vector, but it isn't working!

Here are somethings that might help:
Are all the angles I am going to put into my equations positive? If not, which ones are negative and why?
Are all my vectors positive here? It's hard to tell the way I placed things on the coordinate plane. Which vectors are supposed to be negative, it seems to me that the x component of B (the second 70km one) would be negative is that right?
Am I going about this the right way? I need to break everything down into right triangles right?
 
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  • #2
Which direction is west? North of west doesn't usually mean a vector north of the positive x-axis. But this will be real hard to judge anything unless you actually post your picture here.
 
  • #3
I don't think you can post attachments on this thing, or even photos.
 
  • #4
Towards the left of the y-axis is -x direction and right of the y-axis is +x direction. So the x-component of one of the vectors is negative. Which one is it?
 
  • #5
You can post pictures here.
 
  • #6
Using + = east and north of origin:
Total E-W displacement = (-)50 cos45 + 70 cos 30 = 25.266East of origin
total N-S displacement = 50 sin45 + 70 sin 30 = 70.355 north of origin

Since you're talking in terms of north-south and east-west of origin, you do have right triangles to deal with:
length of resultant = sqrt(25.2662 + 70.3552) = 74.754
angle north of east = tan(-1) (70.355/25.266) = 70.24 degrees

physics + dirt = engineering
 

1. What does it mean for a component vector to be positive or negative?

A component vector is considered positive when it points in the same direction as the chosen coordinate system, and negative when it points in the opposite direction. This is determined by the direction of the arrow on the vector.

2. How are positive and negative angles defined?

In mathematics and physics, angles are typically measured counterclockwise from the positive x-axis, with positive angles lying in the first and second quadrants, and negative angles lying in the third and fourth quadrants. However, in some fields, such as navigation and engineering, angles may be measured clockwise from the positive y-axis. It is important to clarify which convention is being used when discussing positive and negative angles.

3. Can a vector have both positive and negative components?

Yes, it is possible for a vector to have both positive and negative components. This occurs when the vector has components in different directions, such as a force acting on an object at an angle.

4. How do positive and negative angles affect vector addition?

When adding vectors, the angle between them must be taken into account. If the angles are both positive or both negative, the resulting vector will have a positive angle. However, if one angle is positive and the other is negative, the resulting vector will have an angle between them. This is because the negative angle effectively rotates the vector in the opposite direction.

5. Are there any real-world applications of positive and negative component vectors and angles?

Yes, component vectors and angles are commonly used in physics and engineering to analyze and describe the motion and forces acting on objects. They are also used in navigation and mapping to determine the direction and distance between two points. Additionally, they are used in computer graphics and animation to represent and manipulate objects in a virtual space.

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