Objects A and B are at the origin. If object A moves to $(5, - 3)$ $(5 ,-3 )$ and object B moves to $(- 7, 2)$ $(-7 ,2 )$ over $3 s$ $3 s$ , what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

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Answer 1 · 2018-04-02T11:44:11

The relative velocity is $= < - 4, \frac{5}{3} > m s^{- 1}$ $= <-4, 5/3> ms^-1$

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The absolute velocity of $A$ $A$ is $v_{A} = \frac{1}{3} < 5, - 3 > = < \frac{5}{3}, - 1 >$ $v_A=1/3 <5,-3> = <5/3, -1>$

The absolute velocity of $B$ $B$ is $v_{B} = \frac{1}{3} < - 7, 2 > = < - \frac{7}{3}, \frac{2}{3} >$ $v_B=1/3 <-7,2> = <-7/3, 2/3>$

The relative velocity of $B$ $B$ with respect to $A$ $A$ is

$v_{B / A} = v_{B} - v_{A} = < - \frac{7}{3}, \frac{2}{3} > - < \frac{5}{3}, - 1 >$ $v_(B//A)=v_B- v_A=<-7/3, 2/3> - <5/3, -1>$

$= < - \frac{7}{3} - \frac{5}{3}, \frac{2}{3} + 1 >$ $= <-7/3-5/3, 2/3+1>$

$= < - 4, \frac{5}{3} > m s^{- 1}$ $= <-4, 5/3> ms^-1$

Objects A and B are at the origin. If object A moves to (5,−3)(5 ,-3 ) and object B moves to (−7,2)(-7 ,2 ) over 3s3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.