How Do You Calculate Vector Components and Resultant Displacement?

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In summary, vectors have both a magnitude and a direction, and their components represent the magnitude in each direction. In the first problem, the x component would be 810 cos(18) and the y component would be 810 sin(18). In the second problem, the x component would be 23 cos(65) and the y component would be -23 sin(65). In the third problem, the resultant displacement would be the sum of all the individual displacements, which can be found by adding up the respective x and y components.
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hizeme
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Homework Statement


1. A displacement vector has a magnitude of 810m and points at an angle of 18 degrees above the positive x axis, What are the x and y scalar components of this vector?

2. A displacement vector is 23 km in length and directed 65 degrees south of east
What are the components of this vector (East=x South =y)

3. Four members of the Main Street bicycle club meet at a certain intersection on Main Street. The member then start from the same location, but travel in different direction. A short time later, displacement vectors for the four members are:
A=2.0km east B=5.2km north C= 4.9km west D=3.0kmsouth
What is the resultant displacement R for all the members of the bicycle club
r=a+b+c+d



Homework Equations





The Attempt at a Solution


No clue where to start
 
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  • #2
Well the place to start would be to read up on what is meant by components of a vector. Try looking here, for example.
 
  • #3


As a scientist, it is important to understand the concepts and equations related to displacement and vectors. The magnitude and direction of a displacement vector can be represented using trigonometric functions and can also be broken down into its x and y components. In order to find the x and y components of the first displacement vector, you can use the following equations:

x = magnitude * cos(angle)
y = magnitude * sin(angle)

Substituting the given values, we get:
x = 810m * cos(18 degrees) = 780.12m
y = 810m * sin(18 degrees) = 239.28m

For the second question, we can use the same equations but with different values:
x = 23km * cos(65 degrees) = 9.98km
y = 23km * sin(65 degrees) = 21.88km

For the third question, we can use the concept of vector addition to find the resultant displacement. We can represent the given displacement vectors as follows:

A = (2.0km, 0km)
B = (0km, 5.2km)
C = (-4.9km, 0km)
D = (0km, -3.0km)

Adding all these vectors, we get:
R = (2.0km, 0km) + (0km, 5.2km) + (-4.9km, 0km) + (0km, -3.0km) = (-2.9km, 2.2km)

Therefore, the resultant displacement for all members of the bicycle club is (-2.9km, 2.2km). This means that the members have moved 2.9km to the west and 2.2km to the north from their starting point.
 

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