Vector addition problem

In summary, the conversation involved vector addition for four different scenarios: a) 2cm N + 7cm W, b) 5m S + 8cm N, c) 30m/s W + 50m/s S, and d) 5cm N + 7cm W + 9cm S. The answers for b and c were determined by adding the vectors as they are, while for d, the N and S components were added separately and then combined with the W component. As for a), there was something missing so a summary could not be provided.
  • #1
MoreZitiPlease
107
0
a.
2cm N + cm W

b. 5m S+ 8cm N

c. 30m/s W+ 50m/s S

d. 5cm N + 7cm W +9cm S


My answers:

a.7.2
b.9.43
c.58
d.?

I want to know if a,b, and c are right; I don't know d.
 
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  • #2
Well, b and c are correct...I don't know what is a) and for part d) consider the N and S alone, and the "add'' to the W
 
  • #3
Remember that a vector always has both magnitude and direction, so the answer to any vector addition is a vector. An answer that gives only the magnitude is incorrect, unless only the magnitude is asked for.

(a) seems to have something missing, so we can't do that one.

For (b), we have 5m S = -5m N so the sum is

-5m N + 0.08m N = -4.92m N = 4.92m S

For (c) we need to add things as vectors. This gives a resultant vector with magnitude

[tex]\sqrt{30^2 + 50^2) = 58.3[/tex]

The relevant angle from the south direction is

[tex]\tan^{-1}(\frac{30}{50}) = 31^\circ[/tex]

So the full answer is

[tex]58.3\text{~m/s S~}31^\circ\text{W}[/tex]
 
  • #4
How did you get b?
 
  • #5
MoreZitiPlease said:
How did you get b?

A vector x in the south direction is equivalent to a vector -x in the north direction.
 
  • #6
a= 2cm N + 7cm W
 

What is vector addition?

Vector addition is the process of combining two or more vectors to determine the resulting vector. It is used to calculate the total displacement or velocity of an object.

How do you add vectors?

To add vectors, you must first determine their magnitudes and directions. Then, you can use the Pythagorean theorem and trigonometric functions to find the magnitude and direction of the resulting vector.

What are the rules of vector addition?

The rules of vector addition are: 1) Vectors can be added in any order, 2) The commutative property applies (A + B = B + A), 3) The associative property applies ((A + B) + C = A + (B + C)), and 4) Vectors can be added using the parallelogram method or the head-to-tail method.

How do I determine the direction of the resulting vector?

The direction of the resulting vector can be determined using trigonometric functions. For example, if the x and y components of the resulting vector are known, the direction can be found using the inverse tangent function (tan-1(y/x)).

What are some real-life examples of vector addition?

Some real-life examples of vector addition include calculating the total displacement and velocity of a moving object, determining the resultant force on an object, and finding the direction and magnitude of the wind by combining the velocity and direction vectors of individual wind gusts.

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