Differences

This shows you the differences between two versions of the page.

--- 183_notes:examples:vectordecomposition [2014/07/10 19:05] – caballero
+++ 183_notes:examples:vectordecomposition [2014/07/10 19:08] (current) – [Solution] caballero
@@ Line 15: / Line 15: @@
 {{ :183_notes:vectordecomp_w_directions.png?300 }}
-The angle that you know ( $\theta = 35^{\circ}$ ) is the one that the vector makes with the negative y-axis. So the opposite side is the  $x$ -component. Hence,
+The angle that you know ( $\theta = 35^{\circ}$ ) is the one that the vector makes with the negative y-axis. So the opposite side is the  $x$ -component. Hence the above formula do not apply and,
- $r_x = |\vec{r}| \sin(\theta) = 5\:m \sin(35^{\circ}) = 2.87\:m$
+$$ r_x = |\vec{r}| \sin(\theta) = (5\:m) \sin(35^{\circ}) = 2.87\:m$$
+The  $y$ -component is the adjacent side and is negative. Hence,
+ $r_y = -|\vec{r}| \cos(\theta) = -(5\:m) \cos(35^{\circ}) = -4.10\:m$
+where the minus sign was introduced because the measure of the angle was less than 90 $^{\circ}$ .