# A car travels 12 km due north and then 26.2 in a direction 0/( that is supposed to be a circle...

## Question:

A car travels 12 km due north and then 26.2 in a direction 0/( that is supposed to be a circle with a line through it) 67.3 west of north. Find the magnitude of the cars resultant displacement

## Resultant of Vectors:

Resultant of two or more vectors is a single vector which can produce the same effect as the combined vector would do together.

To find the resultant of two vectors first we find the component of each vector along X and Y axis then we can find the resultant by using the cartesian formula.

Let the East West direction is X axis and North South direction be Y axis.

{eq}\vec{r_1}=12 \hat{j} \\ \vec{r_2}=26.2 \sin67.3 \hat{-i}+26.2 \cos67.3 \hat{j} \\ {/eq}

Resultant is given by

{eq}\vec{r}=\vec{r_1} +\vec{r_2} \\ \Rightarrow \vec{r}=12 \hat{j} + 26.2 \sin67.3 \hat{-i}+26.2 \cos67.3 \hat{j} \\ \Rightarrow \vec{r}=26.2 \sin67.3 \hat{-i}+(26.2 \cos67.3 +12) \hat{j} \\ \Rightarrow \vec{r}=24.17 \hat{-i}+(22.11) \hat{j} \\ \Rightarrow |\vec{r}|= \sqrt{24.17^2+22.11^2}=32.76\ m {/eq}