Vector Magnitude and Direction Problem

In summary, the two given vectors have magnitudes of 5.4 m and 3.5 m, and are directed east and 36° west of north, respectively. To find the total magnitude and direction of a + b, the components of each vector are calculated and then added together. For b - a, the components are subtracted and the angle is taken in the second quadrant. The final answers are 7.98 m for magnitude and 20.79° west of east for direction (rounded to the nearest degree).
  • #1
spkenn5
4
0

Homework Statement


Vector has a magnitude of 5.4 m and is directed east. Vector has a magnitude of 3.5 m and is directed 36° west of north. What are (a) the magnitude and (b) the direction (from east) of a + b? What are (c) the magnitude and (d) the direction (from east) of b - a ? Round your angles to the nearest degree.


The Attempt at a Solution



this is what i have attempted so far.
a) ax = 5.4m - 3.5sin36
= 3.34 m
bx = 3.5sin36
= 2.83 m
A = sqrt(3.34^2 + 2.83^2)
= 4.38 m
b) theta = arctan(2.83/3.34)
= 40.27 deg

c) ax = 5.4m + 3.5sin36
= 7.46 m
bx = 3.5sin36
= 2.83 m
A = sqrt(7.46^2 + 2.83^2)
= 7.98 m
d) STUCK.
arctan(2.83/7.46) = 20.79

I am using WileyPlus program, so they are able to detect if my answer is right or wrong. so far i have attempted these answers, and they accepted it EXCEPT the part D. i don't get what i did wrong.

thanks for the help
 
Physics news on Phys.org
  • #2
If you measure the angle in clockwise direction, it should be taken as negative.
 
  • #3
thanks for the reply!

i did the negative also. i input -20.79 and they won't accept it.
 
  • #4
spkenn5 said:
thanks for the reply!

i did the negative also. i input -20.79 and they won't accept it.
They have asked the direction of (b - a), which lies in the second quadrant.
 
  • #5
thanks dude you hit the spot right there!

appreciated it! now i can sleep well.
 

1. What is a vector magnitude and direction problem?

A vector magnitude and direction problem is a type of mathematical problem that involves finding the magnitude (length or size) and direction of a vector, which is a quantity that has both magnitude and direction. Vectors are commonly used in physics and engineering to represent quantities such as velocity, force, and displacement.

2. How do you find the magnitude of a vector?

The magnitude of a vector can be found using the Pythagorean theorem, which states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the other two sides. In the case of a vector, the magnitude is equal to the square root of the sum of the squares of its components (x and y or x, y, and z in three-dimensional space).

3. What is the difference between magnitude and direction?

Magnitude refers to the size or length of a vector, while direction refers to the angle or orientation of the vector in relation to a reference axis. Both magnitude and direction are necessary to fully describe a vector.

4. How do you represent vector magnitude and direction graphically?

Vector magnitude and direction can be represented graphically using an arrow. The length of the arrow represents the magnitude, while the direction of the arrow represents the direction of the vector. The arrow is typically drawn from the origin to the tip, with the angle of the arrow indicating the direction.

5. Can you have a negative vector magnitude?

No, vector magnitude is always a positive quantity. However, the direction of a vector can be negative if it is pointing in the opposite direction of the reference axis. For example, a vector with a magnitude of 5 units and a direction of -30 degrees would be pointing in the negative direction of the reference axis at an angle of 30 degrees.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
533
  • Introductory Physics Homework Help
Replies
16
Views
669
  • Introductory Physics Homework Help
Replies
14
Views
231
  • Introductory Physics Homework Help
Replies
4
Views
523
  • Introductory Physics Homework Help
Replies
2
Views
9K
  • Introductory Physics Homework Help
Replies
3
Views
849
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
23
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
1K
Back
Top