Distance, Displacement and Position Video 3

Distance, Displacement and Position and using trigonometry functions


 by M. Bourne

For the angle θ in a right-angled triangle as shown, we name the sides as:

 hypotenuse (the side opposite the right angle)

  adjacent (the side "next to" θ)

          opposite (the side furthest from the angle)

We define the three trigonometrical ratios sine θ, cosine θ, and tangent θ as follows (we normally write these in the shortened forms sin θ, cos θ, and tan θ):

To remember these, many people use SOH CAH TOA, that is:

Sin θ = Opposite/Hypotenuse,

Cos θ = Adjacent/Hypotenuse, and

Tan θ = Opposite/Adjacent


To show an understand the difference between distance, displacement, and position
To find the resultant of vector addition.
To find the equilibriant of the resultant.
To practice drawing vectors


Blank paper
Graph Paper (if you need graph paper go here)
Pen or pencil


For the following problems use the standard x,y coordinated system. Treat north as the positive y direction and east as the positive x direction.
Using the motions from homework 1, find distance traveled, total displacement, final position (treat the origin as the initial position) the resultant, and the angle of the resultant for the following motions. Also draw the resultant vector for each motion (one square on the graph paper is equal to 1 meter).

Motions from homework 1
a) Walking 10 meters east.
b) Walking 10 meters west.
c) Walking 10 meters south.
d) Walking 20 meters north.
e) Walking 20 meter south.
f) Walking 10 meters east.
g) Walking 25.5 meters west.
h) Walking 17.37 meters north.

Motions for homework3
1. a + b + a
2. a + c + d
3. a + c + g
4. a + f + h
5. c + d + d
6. c - d - d
7. e + f - g
8. h + h + h

Answer the following questions.
1. The equilibriant is a vector that restores the system back to where it started. Mathematically that is expressed as equilibriant = - Resultant. How would you find the equilibriant mathematically for a + b + c? Explain. How would find the equilibriant graphically?
2. Solve for the equilibriant for the eight motions in this homework assignment.
3. If vector a was 10 m at 30 degrees from the positive x axis, how would you find the resultant mathmatically for this motion a + b + c? How would you solve it graphicaly? Which method is easier? which method is more accurate?