Question

Objects A and B are at the origin. If object A moves to `(3 ,6 )` and object B moves to `(6 ,-5 )` over `1 s`, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Answer 1

`vec v_(B w.r.t A)=3 hat i - 11 hat j`

Explanation:

`vec r_i`= initial displacement vector
`vec r_j`=final displacement vector
`vec r_A`=Displacement vector of A
`vec r_B`=Displacement vector of B
w.r.t=with respect to

`vec r_i=vec 0`
`vec r_f=3hati + 6hatj`
`vec r_A= vec r_f - vec r_i`
`vec r_A=3hati + 6hatj`

`vec r_i=vec 0`
`vec r_f=6hati - 5hatj`
`vec r_B= vec r_f - vec r_i`
`vec r_B=6hati - 5hatj`

`vec r_(B w.r.t A) = vec r_B - vec r_A`

`vec r_(B w.r.t A) = 3hati - 11hatj (m)`

`vec v_(B w.r.t A)=(vec r_(B w.r.t A))/t`

`vec v_(B w.r.t A)= (3hati - 11hatj (m))/(1s)`

`vec v_(B w.r.t A)= 3hati - 11hatj (m*s^-1)`

`|vec v_(Bw.r.tA)| = sqrt(130) m*s^-1`