# How Do You Calculate Vector Components and Resultant Displacement?

• hizeme
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.
hizeme

## 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

## The Attempt at a Solution

No clue where to start

Well the place to start would be to read up on what is meant by components of a vector. Try looking here, for example.

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.

## 1. What are the three questions that you can't seem to figure out?

The three questions that I am having trouble figuring out are:

1. How can we effectively combat climate change?
2. What is the cure for cancer?
3. How can we achieve world peace?

## 2. Why are these questions important?

These questions are important because they address major issues that affect our world and the future of humanity. Finding answers to these questions can have a significant impact on our lives and the lives of future generations.

## 3. What are some possible solutions to these questions?

Some possible solutions to combat climate change include reducing carbon emissions, investing in renewable energy, and implementing sustainable practices. For the cure for cancer, solutions may include further research, early detection and prevention methods, and improved access to healthcare. Achieving world peace may involve promoting diplomacy and understanding between nations, addressing social and economic inequalities, and promoting human rights.

## 4. Is there any progress being made towards answering these questions?

Yes, there is ongoing research and efforts being made towards finding solutions to these questions. Many organizations, governments, and individuals are actively working towards addressing these issues and making progress towards finding answers.

## 5. As a scientist, what role do you play in finding answers to these questions?

As a scientist, I play a crucial role in researching and studying these questions to gain a better understanding of the problems and potential solutions. I also collaborate with other scientists and experts to develop and test potential solutions and communicate findings to policymakers and the public.

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