How Do You Calculate Displacement Using Vector Components?

[oldspice1212]

A disoriented physics professor drives a distance 3.40km north, then a distance 3.80km west, and then a distance 1.55km south.

Find the magnitude of the resultant displacement, using the method of components.

Find the direction of the resultant displacement, using the method of components.

I tried drawing it got some weird shape...not a triangle

 

[genericusrnme]

"using the method of components"
Drawing triangles isn't the method of components!

What would the displacement vector look like at each step?

 

[majormaaz]

Just think for a moment; you go north a certain distance, and you also go south a certain distance (not in that order). They are opposite directions, right?
Just try to think of the problem as having ONE vertical vector and ONE horizontal vector.
If you have more than one vector in either dimension, add them up to get one vector.

Then you get your triangle.

 

[oldspice1212]

Shouldn't I subtract the south distance from the north?

 

[Nickie]

Based on the information provided, the resultant displacement can be calculated using the Pythagorean theorem, as the total displacement forms a right triangle. The magnitude of the resultant displacement can be found by taking the square root of the sum of the squared distances traveled in each direction, which would be approximately 5.39km.

To find the direction of the resultant displacement, we can use the inverse tangent function to find the angle formed by the displacement. In this case, the angle would be approximately 22.8 degrees, indicating that the displacement is in a north-west direction.

It is important to note that the method of components is a useful tool for calculating resultant displacements, especially when the displacement involves multiple directions. This method allows us to break down the displacement into its individual components, making it easier to calculate the overall magnitude and direction.