Question

A car is driven 225 km west and then 98 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)?

Answer 1

Step-by-step explanation:

Given

First car travels
`225\ km` west so its position vector is given by

`\vec{r_1}=-225\hat{i}`

then it travels in south-west direction for
`98\ km`

`\vec{r_(21)}=98(-\cos (45)\hat{i}-\sin (45)\hat{j})`

so position vector of
`\vec{r_2}` is

`=\vec{r_(21)}+\vec{r_1}`

`=98(-\cos (45)\hat{i}-\sin (45)\hat{j})-225\hat{i}`

`=-(69.29+225)\hat{i}-69.29\hat{j}`

`=-294.29\hat{i}-69.29\hat{j}`

Magnitude of displacement is given by

`|\vec{r_2}|=√(294.29^2+69.29^2)`

`|\vec{r_2}|=302.34\ km`