Question

You have two vectors, which are 2.59 m at 30.0° north of east and 4.18 m at 60.0° north of west. What is the magnitude in meters (m) of the vector which results from adding these two vectors together?

Answer 1

Answer:$\ec{r}=0.153\hat{i}+4.914\hat{j}$v

Explanation:

Given

Vector 1

$\vec{a}=2.59\left ( cos30\hat{i}+sin30\hat{j}\right )$

Vector 2

$\vec{b}=4.18\left ( -cos60\hat{i}+sin60\hat{j}\right )$

Resultant $\vec{r}=\vec{a}+\vec{b}$

$\vec{r}=2.59\left ( cos30\hat{i}+sin30\hat{j}\right )+4.18\left ( -cos60\hat{i}+sin60\hat{j}\right )$

$\vec{r}=0.153\hat{i}+4.914\hat{j}$

$|r|=4.916$