Vector Addition and Magnitude: Q1 & Q2

In summary, for question 1, the answer is "south of east" because the difference of a vector is calculated by subtracting the components of the second vector from the first vector. In this case, vector B is being subtracted from vector A, so the resulting vector C will have a direction that is opposite to vector B, which points east. Therefore, vector C will point south of east.For question 2, the magnitude of the resultant vector can be found using the Pythagorean theorem, where the hypotenuse is the resultant vector and the legs are the individual vectors A and B. The angle between vector A and the resultant vector can be found using trigonometric functions, and then the magnitude of the resultant vector can
  • #1
Cowtipper
36
0
Question 1:

Homework Statement


Vector A points north and vector B points east. If C = B - A, then vector C points...

A) north of east
B) south of east
C) north of west
D) south of west

Homework Equations





The Attempt at a Solution



I know the answer is "south of east" (or at least I'm 99% sure). But why? I don't understand why, exactly. Can someone please explain? Thanks, I really appreciate the help.

Question 2:

Homework Statement


Vector A is 3.0 units in length and points along the positive x-axis; vector B is 4.0 units in length and points along a direction 150 degrees from the positive x-axis. What is the magnitude of the resultant when vectors A and B are added?


Homework Equations





The Attempt at a Solution



This is an image I made that I think shows what they are talking about. From there, I'm not too sure where to go...

Thanks again.
 
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  • #2
For question 1, how is the difference of a vector defined. Or how have you been shown to calculate the difference of a vector.

For question 2, you haven't posted any imagebut what have you learned about vector addition and finding the magnitudes of vectors?
 
  • #3
A diagram is your best friend.
 

1. What is a vector in physics?

A vector in physics is a quantity that has both magnitude and direction. It is represented by an arrow with its length indicating the magnitude and its direction indicating the direction of the quantity. Examples of vectors in physics include force, velocity, and displacement.

2. How do you add and subtract vectors?

When adding or subtracting vectors, you need to consider both their magnitude and direction. To add vectors, you can use the head-to-tail method where you place the tail of the second vector at the head of the first vector, and the resultant vector is drawn from the tail of the first vector to the head of the second vector. To subtract vectors, you can use the head-to-head method where you place the tail of the second vector at the head of the first vector, and the resultant vector is drawn from the head of the second vector to the tail of the first vector.

3. What is the difference between displacement and distance?

Displacement is a vector quantity that refers to the change in position of an object from its initial position to its final position, taking into account both magnitude and direction. On the other hand, distance is a scalar quantity that refers to the total length of the path traveled by an object, regardless of its direction. In other words, displacement is a specific type of distance that takes into account the direction of movement.

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

The magnitude of a vector can be calculated using the Pythagorean theorem, where the length of the vector is the hypotenuse of a right triangle formed by its x and y components. To find the direction of a vector, you can use the inverse tangent function (tan-1) to find the angle between the vector and the horizontal axis.

5. What is the difference between speed and velocity?

Speed is a scalar quantity that refers to the rate of change of distance over time. On the other hand, velocity is a vector quantity that refers to the rate of change of displacement over time. This means that velocity takes into account the direction of movement, while speed does not. For example, a car traveling at 60 mph has a speed of 60 mph, but its velocity could be 60 mph east.

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