Question

How can i calculate distance and displacement here?

the earth rotates around the sun in one year, if the distance between the earth and the sun is 150 million km ,find the distance and the displacement during:
A. a quarter year
B. two years and half

Answer 1

`s_1=75pi`million km; `|A_1B_1|=212.132`million km
`s_2=750pi`million km; `|A_2B_2|=300`million km

Explanation:

Given:
Distance between earth and sun
`150`million km

A) distance and displacement during the quarter year

`r=150`million km
angular rotation
`thea_1=pi/2`

distance travelled
`s_1=rtheta_1`
`s_1=150xx(pi)/2`
`s_1=75pi`million km
displacement
`vecs_1=vec(AB)`
`A_1-=(r,0)`
`B_1-=(0,r)`
`vec(A_1B_1)=(0-r)hati+(r-0)hatj`
`vec(A_1B_1)=-rhati+rhati`
magnitude is
`|A_1B_1|=sqrt(r^2+r^2)=sqrt2r`
`|A_1B_1|=sqrt2xx150`
`|A_1B_1|=212.132`million km

A) distance and displacement during the quarter yeartwo years and half

`r=150`million km
angular rotation
`thea_2=5pi`

distance travelled
`s_2=rtheta_2`
`s_2=150xx5pi`
`s_2=750pi`million km
displacement
`vecs_2=vec(A_2B_2)`
`A_2-=(r,0)`
`B_2-=(-r,0)`
`vec(A_2B_2)=(-r-r)hati+(0-0)hatj`
`vec(A_2B_2)=-2rhati`
magnitude is
`|A_2B_2|=2r`
`|A_2B_2|=2xx150`
`|A_2B_2|=300`million km