How Do You Calculate Displacement from a Vector Diagram?

[andyman21]

Bob gets in his car and drives at an average speed of 25 miles per hours (mph) for 4.0 hours due north. He then turns, and drives 75 miles directly east. At that point, Bob turns again and drives 50 miles due south and stops. Draw a diagram with a coordinate system and finds Bob's total displacement for the entire trip.

First off to figure out the north direction I used the average velocity formula but instead solved for the displacement of x or change. So it would be distance traveled times the time elapsed or time interval which is 4. (25x4=100). So he goes 100 miles directly north, 75 miles east, and 50 miles south.

From this point I always get confused on what to do. I get confused easily with vector problems.

Any help would be greatly appreciated. Thank you in advance.

 

[gneill]

Bob gets in his car and drives at an average speed of 25 miles per hours (mph) for 4.0 hours due north. He then turns, and drives 75 miles directly east. At that point, Bob turns again and drives 50 miles due south and stops. Draw a diagram with a coordinate system and finds Bob's total displacement for the entire trip.

First off to figure out the north direction I used the average velocity formula but instead solved for the displacement of x or change. So it would be distance traveled times the time elapsed or time interval which is 4. (25x4=100). So he goes 100 miles directly north, 75 miles east, and 50 miles south.

From this point I always get confused on what to do. I get confused easily with vector problems.

Any help would be greatly appreciated. Thank you in advance.

Draw the various displacements on a coordinate system (you can place Bob's starting point at the origin. The total displacement will be the vector from his starting location to his ending location.

 

[andyman21]

There was a similar problem that I found on this site and the guy for some reason subtracted the two vertical slopes. So i would do 100-50 miles. Then I would use those two displacements and to find the total displacement do the pathagrien theorem correct?

 

[gneill]

There was a similar problem that I found on this site and the guy for some reason subtracted the two vertical slopes. So i would do 100-50 miles. Then I would use those two displacements and to find the total displacement do the pathagrien theorem correct?

For someone who is just learning the basics of vectors it is often very helpful to draw the diagram first. Then the "operations" that are performed (such as combining the like components of the vectors) becomes something you can visualize on the diagram.

The total displacement is given by the vector sum of the individual displacement vectors, and is also equal to the difference between the final position and the initial position.

Can you write, say in (x, y) format, the three displacement vectors involved?

 

[andyman21]

The three individual displacement vectors are, starting from Bobs origin, is he head north 100 mi(up y-axis), then go directly east 75 miles(right on the graph or x-axis), then drives 50 miles south(down the y-axis).

 

[gneill]

The three individual displacement vectors are, starting from Bobs origin, is he head north 100 mi(up y-axis), then go directly east 75 miles(right on the graph or x-axis), then drives 50 miles south(down the y-axis).

Okay, but in (x,y) format? For example: d1 = (0 , 100) , or, d1 = 0i + 100j

 

[andyman21]

I am sorry I guess I just don't understand on what to give you here, I apologize its my first physics class.

 

[gneill]

The three individual displacement vectors are, starting from Bobs origin, is he head north 100 mi(up y-axis), then go directly east 75 miles(right on the graph or x-axis), then drives 50 miles south(down the y-axis).

I am sorry I guess I just don't understand on what to give you here, I apologize its my first physics class.

No need to apologize! We've all been there, done that!

The (x,y) format is shorthand for components that make up a vector in a given Cartesian coordinate system. The xi + yj format is similar. The "i" and "j" are simply indicators of the directions that the given component represents. In this case i --> eastwards, j --> northwards.

In your case the coordinate system pertains to distances North-South and East-West. The origin is at Bob's starting location. The first component represents displacement in the East-West direction, and the second represents displacement in the North-South direction.

In the North-South direction positive values are northward distances while negative values are southward distances. Similarly, in the East-West direction a positive value represents a displacement eastwards, while a negative value would be a displacement westwards. Bob's first leg of his trip, a 100 mile northward drive, could be specified as: (0, 100) with units of miles.