Question

Objects A and B are at the origin. If object A moves to `(2 ,1 )` and object B moves to `(5 ,2 )` over `4 s`, what is the relative velocity of object B from the perspective of object A?

Answer 1

`sqrt10/4` in the direction given by `tan^(-1)(1/3)`

Explanation:

As the displacement for object A is `(2,1)`

and displacement for object B is `(5,2)`

relative displacement of B w.r.t. A is `(5-2,2-1)` or `(3,1)`

as compared to `(0,0)` at the start of `4` seconds

Hence, relative velocity of object B from the perspective of object A is `3/4hati+1/4hatj`

or `sqrt((3/4)^2+(1/4)^2)=sqrt10/4` in the direction given by `tan^(-1)((1/4)/(3/4))=tan^(-1)(1/3)`