How do I solve this problem? Finding the resultant vector

In summary, the conversation discusses finding the resultant displacement both graphically and algebraically after making various displacements in the xy-plane. The homework equations of addition of vector components are used to solve this problem. There is a mistake in the attempt at a solution, as Bx should be -30 rather than 30. The correct answer is 97mm at 158°.
  • #1
a321
3
0

Homework Statement



Starting at the origin of coordinates, the following displacements are made in the xy-plane (that is, the displacements are coplanar): 60 mm in the +y-direction, 30 mm in the Ñx-direction, 40 mm at 150°, and 50 mm at 240°. Find the resultant displacement both graphically and algebraically.

Homework Equations



Addition of vector components

The Attempt at a Solution



I tried to break it into components:
Ax=0
Bx=30
Cx=-34.6
Dx= -25

Ay=60, By=0, Cy=20, Dy=-43.3

However The answer is 97mm at 158°
How did they get this answer?

THANKS for your help!
 
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  • #2
welcome to pf!

hi a321! welcome to pf! :smile:

shouldn't Bx be minus 30 ? :wink:​
 
  • #3
Oh wow! Yes you are right! thanks so much!
 

1. How do I find the resultant vector?

To find the resultant vector, you need to add all the individual vectors together. This can be done by breaking each vector into its horizontal and vertical components, adding them separately, and then using the Pythagorean theorem to find the magnitude of the resultant vector. Alternatively, you can use trigonometric functions to find the magnitude and direction of the resultant vector.

2. What if I have more than two vectors?

If you have more than two vectors, you can still use the same method of breaking them into horizontal and vertical components and adding them together. You can also use the parallelogram method, where you draw the vectors to scale on a graph and then construct a parallelogram, with the resulting diagonal being the resultant vector.

3. Can I use the same method for vectors in different directions?

Yes, the method of breaking vectors into horizontal and vertical components and adding them together can be used for vectors in any direction. Just make sure to use the correct trigonometric functions to find the magnitude and direction of each component.

4. How do I represent the resultant vector?

The resultant vector can be represented by an arrow pointing in the direction of the vector, with the length of the arrow representing the magnitude of the vector. You can also use vector notation, such as R for the resultant vector.

5. What if the vectors are in three dimensions?

If the vectors are in three dimensions, you can still use the same method of finding the resultant vector by breaking them into their x, y, and z components and adding them together. However, instead of using the Pythagorean theorem, you will need to use the three-dimensional version of the theorem to find the magnitude of the resultant vector.

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