6-6: Vector Addition

"Good evening, I'm Chevy Chase and you're not."



So folks, it's about 1:20 am right about now and I'm consequently not really in a festive mood. Therefore, let's get down to business (TO DEFEAT...THE HUNS!). 6-6 really isn't that bad; it's basically just adding vectors or determining the magnitude and direction of a given vector. But, for the sake of your knowledge, my blog grade, and Sam, let's start at square one....

A vector has both magnitude (length in absolute value) and direction (measured in the angle from the vector to the horizontal axis). Here's the basic "anatomy" of the vector:















The sign for vectors is this:





Okay, so now that we've got the basics down, we can get to vector addition. If you already have two vectors, you can add them (by putting the tip of one to the tail of the other......larry, don't be immature) and get a resultant vector. Sweet italic use, huh? Anyways, here's an example formulated by your resident genius himself, me.























You can see the necessary steps here: First find the magnitude of the resultant vector, then determine the angle of its direction using the given information. This particular vector will have a magnitude of 16.547 ft and a direction of 54.031 degrees. CHYEA.

Alright boys and girls, there's really one more key component of the lesson: deriving the components of a resultant vector from that vector itself. That is, if we have a vector, we can determine the two other vectors that form it when added together....like so:




















Use the nifty little formula and it's pretty self-explanatory.

















NOW IT'S PROBLEM TIME LITTLE KIDDIES

Let's say that on a particular football play, Larry, using his god given athletic ability, first runs 7 yards at an angle of 48 degrees from the horizontal axis and then sharply cuts (as only he can) at an angle of 108 degrees for 6 more yards. Following this brilliant display football prowess, Paul, the starting varsity quarterback (replacing your blogger himself and following in his noble footsteps), reads the Cover 3 defense and decides to hit Larry on the aforementioned intermediate route before the strongside linebacker can cover him (...excuse me, TRY to cover him....I mean, this is Larry the receiving GOD we're talking about here). So then, after that huge digression, determine the resultant vector for the throw Paul needs to make to Larry for the presumably solid play! Ready....BREAK!
(Oh yeah, it looks like this.....hahaha)



















Done? Okay, here's the method of solution to this unbearably sweet problem:

We're done.

Well, except for this: http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

this:

(As you can tell, I was the "N"....in...... NOMAR!!!!!!!!.......GARCIAPARRA!!!!)

and this: REMINDER TO MICHELLE

G'night everybody.