How to calculate resultant vector angle?

In summary, the conversation discusses finding the resultant displacement of a person walking on a path with four straight lines at different angles and lengths. The first part of the problem was solved, but the second part asks for the direction of the displacement measured from due west. The correct method is to add or subtract 180 degrees from the angle measured from due east.
  • #1
euphtone06
22
0
1. A person walks in a path which consists of four straight lines at different angles and lengths as seen in the attached image. http://img253.imageshack.us/img253/244/problemlt5.gif
The first part of the problem was to find the resultant displacement which was found to be 512.8. The second part asks what is the direction measured from due west, with counterclockwise being in the positive direction of the person's resultant displacement?

The Attempt at a Solution


I am having a hard time understanding what the problem means by measured from due west I found the angle of the typical resultant displacement to be 237.26 degrees but this answer was wrong. Is it simply adding +/- 180 for due west? I am confused
 
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  • #2
euphtone06 said:
I am having a hard time understanding what the problem means by measured from due west
For example, if the displacement was due east it would be 180 degrees as measured from due west.
I found the angle of the typical resultant displacement to be 237.26 degrees but this answer was wrong.
What are you measuring your angle with respect to? (From due east, I presume.)
Is it simply adding +/- 180 for due west?
Yes, it's as simple as that. But draw a careful diagram to figure it out.
 
  • #3
Yes I measured the angle from due east so 237.26-180= 57.26 would be my answer from due west?
 
  • #4
Sounds good to me. (I didn't check your original answer though.)
 

FAQ: How to calculate resultant vector angle?

1) What is a resultant vector angle?

A resultant vector angle is the angle between the resultant vector (the sum of two or more vectors) and a reference axis. It represents the direction of the resulting vector.

2) How do you calculate the resultant vector angle?

The resultant vector angle can be calculated using the trigonometric function tangent (tan). First, calculate the x and y components of the resultant vector. Then, divide the y component by the x component to find the tangent of the angle. Finally, take the inverse tangent (arctan) of the calculated value to find the resultant vector angle.

3) Can the resultant vector angle be negative?

Yes, the resultant vector angle can be negative. It depends on the direction of the resultant vector in relation to the reference axis. A positive angle is measured in a counterclockwise direction, while a negative angle is measured in a clockwise direction.

4) What is the reference axis for calculating the resultant vector angle?

The reference axis can vary depending on the specific problem or context. It is typically chosen based on convenience or the direction of the given vectors. For example, if the given vectors are in the x-y plane, the reference axis may be the x-axis.

5) Are there any other methods for calculating the resultant vector angle?

Yes, there are other methods for calculating the resultant vector angle, such as using the dot product or the cross product. These methods may be more useful for more complex or three-dimensional problems. However, the trigonometric method using the tangent function is the most common and straightforward approach.

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