Question

Objects A and B are at the origin. If object A moves to `(-6 ,7 )` and object B moves to `(-6 ,-1 )` over `3 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

`8/3ms^-1`

Explanation:

Relative velocity is a vector quantity. Lets check component wise:

• x-component:
  Both the bodies have moved to the same vertical line, namely `x= -6` line. Hence their x-components of the velocities are same.

• y-component:
  The distance between their final positions is: `(7-(-1)) = 8" m"`
  Hence the relative velocity along y-axis is: `8/3 ms^-1`

Hence the relative velocity is `8/3 ms^-1` along y-axis.

Answer 2

`v_A=2,67 " m/s"`

Explanation:

`"displacement=8 meters"`

`v_A=("displacement")/("time")`

`v_A=8/3`

`v_A=2,67 " m/s"`

Answer 3

In 3s displacement of A from (0.0) to (-6,7) `=vecd_A=(-6hati+7hatj)m`
Velocity of A , `vecV_A=vecd_A/3=1/3(-6hati+7hatj)m/s`

In 3s displacement of B from (0.0) to (-6,-1) `=vecd_B=(-6hati-hatj)m`
Velocity of B, `vecV_B=vecd_B/3=1/3(-6hati-hatj)m/s`
The relative velocity of object B from the perspective of object A
is `vecV_B-vecV_A=1/3(-6hati-hatj+6hati-7hatj)=-8/3hatjm/s`
So magnitude of relative velocity is `8/3m/s` and it is directed towards negative direction of y-axis i.e. `270^o` with positive direction of X-axis