How to Calculate Magnitude and Direction for Orv's Walk?

In summary: It should be drawn as a triangle with one side being 312 m long and the other side being 220 m long. The angle between these two sides is 45 degrees.
  • #1
lalahelp
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0

Homework Statement


Orv walks 312 m due east. He then continues walking along a straight line, but in a different direction, and stops 220 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
What is the magnitude?
What is the direction ___________ ° counterclockwise from the +x-axis



Homework Equations


C=squareroot of 312^2+220^2
What equation to use to find direction??

The Attempt at a Solution


C= Magnitude= 381.76 m why is my magnitude wrong?
 
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  • #2
A good idea here is to read the problem carefully, and/or make a simple diagram.
You're correct in using the Pythagorean theorem for this problem, but you're using it incorrectly. Remember that the form is a^2 + b^2 = c^2, where c is the hypotenuse.

In the problem statement, you're given a = 312 meters (The distance walked east -- one of the legs of the triangle), and c = 220 meters (The distance in a straight line from the starting point -- the hypotenuse).

This means that what you need to find here is b, not c.
 
  • #3
As with regards to your direction issues, once you have your three sides figured out, use your trig laws (soh cah toa).

If you've never heard of them, it goes:
"soh" - sin = opposite / hypotenuse
"cah" - cosine = adjacent / hypotenuse
"toa" - tangent = opposite / adjacent

And you should get the right answer.
Cheers

EDIT: or your sin/cosine laws. I didn't work through the problem myself, I just assumed based on the level it was a right angle triangle.
 
  • #4
Gordanier said:
EDIT: or your sin/cosine laws. I didn't work through the problem myself, I just assumed based on the level it was a right angle triangle.

Same. Now that I look at it (through my sleepy eyes), the 'hypotenuse' is shorter than one of the legs, and by a good bit, too...
 
  • #5
I can't take the square root of a negative number for the magnitude... Is there another way to solve this...
 
  • #6
lalahelp said:

Homework Statement


Orv walks 312 m due east. He then continues walking along a straight line, but in a different direction, and stops 220 m northeast of his starting point. How far did he walk during the second portion of the trip and in what direction?
What is the magnitude?
What is the direction ___________ ° counterclockwise from the +x-axis

Did you ever draw it?
 

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  • #7
@:AC130NAV: The problem states that the final position was 220 m from the starting point in an north easterly direction, so your drawing is not correct.
 
Last edited:

1. What is magnitude and direction?

Magnitude and direction refer to the two components of a vector quantity. Magnitude is the numerical size or value of the vector, while direction is the angle or orientation of the vector.

2. How are magnitude and direction represented?

Magnitude is typically represented by the length of the vector in a graph or diagram, while direction is represented by an arrow pointing in the direction of the vector.

3. What is the difference between scalar and vector quantities?

Scalar quantities have only magnitude and no direction, while vector quantities have both magnitude and direction. Examples of scalar quantities include temperature and time, while examples of vector quantities include force and velocity.

4. How do you calculate the magnitude of a vector?

The magnitude of a vector can be calculated using the Pythagorean theorem, which states that the square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides. In the case of a 2-dimensional vector, the magnitude can be found by taking the square root of the sum of the squares of the x- and y-components of the vector.

5. How is direction measured in vectors?

Direction in vectors is measured in degrees or radians, with 0 degrees usually representing the positive x-axis and 90 degrees representing the positive y-axis. Direction can also be measured in terms of angles above or below the x-axis, or in terms of the horizontal and vertical components of the vector.

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