• Component Method of Summing Vectors

Pre-requisite skills:  Understanding of the Pythagorean Theorem.  Understanding of the arctangent helpful.

Approximate completion time:  Under an hour.

Provide sufficient detail to verify that the assignment was completed in a meaningful manner.

Applet by Fu Kwun Hwang

(a) What happens?   

(b)  From what you see, can you determine why the head-to-tail and parallelogram methods are identical?

2.  Consider the following physical problem:  Suppose an airplane has a top speed of 200 mph.  It attempts to fly 45 degrees West of North. 

(a) Calculate the component vectors of the velocity vector of the plane as if it experienced no wind. 

(b) Using the applet, draw this vector.  On a sheet of graph paper, draw the same vector.

3.  Unfortunately, the airplane experiences a win of 80 mph pointing East. 

(a) Draw a vector representing the wind velocity on both the applet and the same sheet of graph paper.

(b) The applet will add the two vectors to produce the resultant velocity vector.   On the same sheet of graph paper, draw the vector shown in the applet window.   By examining this resultant vector, will the wind increase or decrease the speed of the plane?

(c) Which direction will the airplane take, and what will be its ultimate speed?

Helpful Resources

1. Vector Addition and Subtraction by Wesley Dean.
2. Vectors and Motion in Two Dimensions by Tom Henderson.
3. Vector Illuminations by Ron Greene.
4. Sum of Vectors by Phillip Dukes. (Assignment)
5. Vector Math Worksheet by Gary Richert (Assignment)
6. Vectors by Angel Franco Garcia. (in Spanish)
7. Zona Land's Vectors by Ed Zobel.

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