Vectors and Projectiles Legacy Problem #12 Guided Solution

The skill being targeted on this problem is the skill of being able to determine the components of a vector if given a vector's magnitude and direction. When we mean component, what we mean is the effect of that vector in a given direction. So if a cave explorer walks at 349 meters and 253 degrees, that cave explorer is walking both south and west, 349 meters total. What we wish to know is how much of that vector's displacement is towards the south and how much of it is towards the west. What's the effect of that vector in the southerly and the westerly direction? The shortcut method of determining the answer to the question is to use the magnitude and the direction in the equations that go something like this. The AX vector for vector A, that is the horizontal component for vector A, AX, is equal to A's magnitude times the cosine of theta, where theta is the angle that that vector makes counterclockwise with east. That's in fact one reason why we use such an odd notation or convention for direction. Now if you wish to find the vertical component or the y component, the AY of vector A, then you take A's magnitude and you multiply by the sine of theta, where theta is the counterclockwise angle of rotation with due east. Now these two equations, AX equal A cosine theta and AY equal A sine theta, can always be used as long as theta is at the counterclockwise angle of rotation from east. Now sometimes you'll get a negative value out of these calculations, and that negative value simply means that for an X component that is directed west, and for a Y component that is directed south. An easterly component will always come out positive, a northerly component will always come out positive.