Question

a body moves 4 km east then 4km south and then an additional distance in an unknown direction .its final position is 8 km east of starting point the magnitude of third leg of the journey is

Answer 1

Given:

A body moves 4 km east then 4km south and then an additional distance in an unknown direction .Its final position is 8 km east of starting point.

To find:

Magnitude of third leg of journey ?

Calculation:

These kind of problems can be easily solved with the help of vectors.

When body moves 4 km east:

$\therefore \: \vec{r1} = 4 \hat{i}$

When body moves 4 km south:

$\therefore \: \vec{r2} = 4( - \hat{j})$

Let third leg of journey be $\vec{r3}$:

Now , since the net position of body is 8 km east of starting point :

$\therefore \: \vec{r} = \vec{r1} + \vec{r2} + \vec{r3}$

$\implies \: 8 \hat{i} = 4 \hat{i} + 4( - \hat{j}) + \vec{r3}$

$\implies \: 8 \hat{i} = 4 \hat{i} - 4\hat{j}+ \vec{r3}$

$\implies \: \vec{r3} = 4 \hat{i} + 4 \hat{j}$

$\implies \: | \vec{r3} | = \sqrt{ {4}^{2} + {4}^{2} }$

$\implies \: | \vec{r3} | = \sqrt{ 16 + 16 }$

$\implies \: | \vec{r3} | = \sqrt{32}$

$\implies \: | \vec{r3} | = 4 \sqrt{2} \: km$

So, magnitude of 3rd leg of journey is 4√2 km.

Answer 2

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