Calculating displacement in 1D and 2D - Anne Elizabeth Franck | Library

It is important to establish a frame of reference when we want to measure something.  Basically we have to decide what is zero and what are different directions are.  When measuring displacement in two dimensions the easiest way to create a frame of reference is to map your information on a grid.  

To the left we can see the route from Diamond Ranch to the Starbucks at Rio Rancho from Google maps.  According to Google maps the route (the blue line) has a distance of 2.8 km, but we want to find the displacement (the orange line).  First we establish a frame of reference, by putting the map on a grid.  We set the location of Diamond Ranch at (0,0).  Our x axis runs from  west to east.  Our y axis runs from south to north.  Each square represents 10,000 m2 (100 m a side)

By counting the squares we can see that the displacement is 1700 m or 1.7 km east and 750 m or 0.75 km north.  To calculate the total magnitude of the displacement we can use the Pythagorean theorem:

d2 = x2+y2
x = 1.7 km
y = 0.75 km

d2 = (1.7 km)2+(0.75 km)2
d2 = 2.89 km2 +0.5625 km2
d2 = 3.4525 km2
d = 1.9 km

We could use trigonometry to figure out the angle of displacement as well, but we will save that extra calculation for another day.

Solve the following displacement problems.  Make sure you are answering with the correct units.  

An object moves from point A to point B to point C, then back to point B and then to point C along the line shown in the figure to the right.

Required

1

Find the distance covered by the moving object.

Required

1

Find the magnitude and direction of the displacement of the object.

An object moves from point A to point C along the rectangle shown in the figure to the right.

Required

1

Find the distance covered by the moving object.

Required

1

Find the magnitude of the displacement of the object.

An object moves from point A to B to C to D and finally to A along the circle shown in the figure to the right.

Required

1

Find the distance covered by the moving object.

Required

1

Find the magnitude of the displacement of the object.

An object moves from point A to B to C to D along the circle shown in the figure to the right.

Required

1

Find the distance covered by the moving object.

Required

1

Find the magnitude of the displacement of the object.

An object moves along the grid through the points A, B, C, D, E, and F as shown below.

Required

1

Find the distance covered by the moving object.

Required

1