Help with Vector Components: Finding Magnitude and Direction

[godkills]

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What are the magnitude and direction of the total displacement for the treasure hunt illustrated in Figure 3-9? Assume each pace is .750 m in length.

Question found in Physics 4th edition James S. Walker.

My question is when finding the components of vector C how do you find the angles and use the cos and sin? Or do you use tan? I honesty was lost because there was no example in the book that covered this particular material. There is no angle that was given or anything like that how can I find the components of C? And also when finding the angle for Vector D i had some troubles such as which numbers do I use?

Components of A = A_x = 0 A_y = 3.75

Components of B = B_x = 2.25 B_y = 0

Please guide me through this I am honesty lost in what formulas do I use and where is the angles? D=

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[jhae2.718]

For the direction of C, what does southeast correspond to on a unit circle? (You can take the reference angle here...)

Then, what functions relate a distance and an angle to its components/projections?

After you find the angle for C and take the vector sum to get D, you can find the angle of D by relating its components. What trig function relates the x and y components of a triangle?

 

[godkills]

45 degrees so C_x = 2.12 C_y = -2.12

D = 4.66 m angle 20.5

pyth therom

 

[jhae2.718]

You also need to take into account what direction the vector points. C is points to the right and down, so what should the signs of the components of C be?

 

[rwisz]

I can provide some guidance on how to find the magnitude and direction of vector components. First, let's define what vector components are. Vector components are the individual parts of a vector that act in different directions, usually at right angles to each other. In this case, the vector components are Ax and Ay for vector A, and Bx and By for vector B.

To find the magnitude of a vector component, we can use the Pythagorean theorem, which states that the magnitude of a vector is equal to the square root of the sum of the squares of its components. So for vector A, its magnitude would be:

|A| = √(Ax^2 + Ay^2)

To find the direction of a vector component, we can use trigonometric functions such as sine, cosine, and tangent. In this case, we can use cosine and sine to find the direction of vector A:

θ = arctan(Ay/Ax)

Where θ is the angle between the vector and the x-axis. Similarly, for vector B, we can use:

θ = arctan(By/Bx)

Now, for vector C, we can use the same method to find its magnitude and direction. We can break vector C into its x and y components by using the given angle of 30 degrees and the given magnitude of 5.5 paces. So, the x component of vector C would be:

Cx = 5.5 cos 30 = 4.77

And the y component would be:

Cy = 5.5 sin 30 = 2.75

To find the magnitude of vector C, we can use the Pythagorean theorem again:

|C| = √(Cx^2 + Cy^2) = √(4.77^2 + 2.75^2) = 5.50 paces

To find the direction of vector C, we can use the same method as before:

θ = arctan(Cy/Cx) = arctan(2.75/4.77) = 30.3 degrees

For vector D, we can use the same method to find its magnitude and direction. We can break vector D into its x and y components by using the given angle of 135 degrees and the given magnitude of 4.5 paces. So, the x component of vector D would be:

Dx =