# Vector components - displacement

• shawli
In summary, the train travels at a constant speed of 100km/h for a total of 1.5 hours, changing directions at different intervals. Using vector components and the Pythagorean theorem, the average velocity is found to be 29.4 km/h at 41 degrees north of east.
shawli

## Homework Statement

A train moving at a constant speed of 100km/h travels east for 40min, then 30o east of north for 20 min, and finally west for 30min. What is the train's average velocity for the trip?

## The Attempt at a Solution

I think I have to calculate displacement from the given velocities, using vector components for 100km/h [30o E of N]. Then I find the total x displacement and total y displacement and divide by time (1.5h) to find the x and y velocities. I'm not sure what to do after this :S.

shawli said:
Then I find the total x displacement and total y displacement and divide by time (1.5h) to find the x and y velocities.
That will give you the components of the average velocity. Find the magnitude of that vector.

Oh , I have to use Pythagorean theorem to find the resultant vector, right?

I divide that value by 1.5hr.

And finally I can find the direction by using the arctangent of the displacement components?

I end up getting 29.4 km/h [41 degrees north of east] , but I'm not sure if it's correct since I haven't been given answers to the problem.

shawli said:
Oh , I have to use Pythagorean theorem to find the resultant vector, right?

I divide that value by 1.5hr.

And finally I can find the direction by using the arctangent of the displacement components?
That's right.

I end up getting 29.4 km/h [41 degrees north of east] , but I'm not sure if it's correct since I haven't been given answers to the problem.
Looks good to me!

Last edited:
Thanks a ton!

## 1. What are vector components?

Vector components are the individual parts of a vector that describe its magnitude and direction. They are typically represented by two or three numbers, depending on the dimensionality of the vector, and are used to calculate the overall vector using mathematical operations.

## 2. What is displacement in relation to vector components?

Displacement is a vector quantity that describes the change in position of an object. It is calculated by finding the difference between the initial and final positions of the object, taking into account the direction of movement. Vector components can be used to represent the displacement of an object in a specific direction.

## 3. How are vector components calculated?

Vector components can be calculated using trigonometry and the Pythagorean theorem. The magnitude of the vector is calculated by finding the square root of the sum of the squared components, while the direction is determined using inverse trigonometric functions.

## 4. What is the difference between scalar and vector components?

Scalar components only have magnitude, while vector components have both magnitude and direction. Scalar components are represented by a single number, while vector components are represented by multiple numbers or symbols.

## 5. How are vector components used in real-world applications?

Vector components are used in many scientific fields and industries, such as engineering, physics, and navigation. They are used to calculate forces, velocities, and displacements in various systems and can also be used in computer graphics and game development to simulate movement and physics.

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