Objects A and B are at the origin. If object A moves to $(- 2, 2)$ $(-2 ,2 )$ and object B moves to $(7, 9)$ $(7 ,9 )$ 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 · 2018-05-29T17:36:48

The relative velocity is $= < 3, \frac{7}{3} > m s^{- 1}$ $=<3, 7/3 > ms^-1$

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The absolute velocity of $A$ $A$ is

$v_{A} = \frac{1}{3} < - 2, 2 > = < - \frac{2}{3}, \frac{2}{3} > m s^{- 1}$ $v_A= 1/3 <-2, 2 > = <-2/3, 2/3> ms^-1$

The absolute velocity of $B$ $B$ is

$v_{B} = \frac{1}{3} < 7, 9 > = < \frac{7}{3}, 3 > m s^{- 1}$ $v_B= 1/3 <7, 9> = <7/3, 3> ms^-1$

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

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

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

$= < 3, \frac{7}{3} > m s^{- 1}$ $= <3, 7/3 > ms^-1$

Objects A and B are at the origin. If object A moves to (-2 ,2 )(−2,2)(-2 ,2 ) and object B moves to (7 ,9 )(7,9)(7 ,9 ) over 3 s3s3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.