Session 4, part 2 -- Vector Addition

Vector quantities can be visualized as arrows. Adding two arrows in the same direction gives a larger arrow. Likewise, adding two (similar) vector quantities (say, 2 velocities) yields a larger velocity.

Subtracting vector quantities is simply adding one vector to a negative vector, resulting in a smaller vector.

Imagine walking on a "people mover". If you walk in the direction of the mover's velocity, you ultimately have a greater velocity than the mover itself (with respect to the people observing on the side). If you walk in the OPPOSITE direction to the mover's velocity, which is a pretty lame thing to do, you will have a velocity that is less than that of the mover itself.

How about adding vectors at angles? This is a bit trickier. See the second slide above.

If two vectors, A and B, are at a right angle to each other, the "resultant vector" C is given by the Pythagorean Theorem:

A^2 + B^2 = C^2

and the angle between C and the horizontal is given by the tangent relationship.

tan (angle) = OPP / ADJ = A/B

so that the angle itself is given by the inverse (or arc) tangent of A/B:

angle = arctan (A/B)

If trigonometry is not something you remember that well, check out:

http://howdoweknowthat.blogspot.com/2009/07/how-far-away-is-that.html


Some problems to try:

1. A flagpole makes an angle of 55 degrees with respect to horizontal, as measured from a point 10-m away. How tall is the flagpole?

2. Add 2 vectors together: 10 and 20, at a right angle to each other. Find the resultant vector and the angle as measured from the 20 vector.

3. Imagine trying to cross a river, 100-m wide with a current of 2 m/s. If you head out in your motorboat at 10 m/s, find the following:

a. how long it will take you to cross
b. how far downstream you will be
c. the angle you take with respect to your original path

In this problem, there is NO acceleration - rather, the velocities are added simultaneously (or "concurrently").