Objects A and B are at the origin. If object A moves to $(3, - 7)$ $(3 ,-7 )$ and object B moves to $(2, 9)$ $(2 ,9 )$ over $2 s$ $2 s$ , 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 · 2017-09-08T06:33:52

The relative velocity of $B$ $B$ with respect to $A$ $A$ is $= < - \frac{1}{2}, 8 > m s^{- 1}$ $= <-1/2, 8>ms^-1$

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

The absolute velocity of $B$ $B$ is $v_{B} = \frac{1}{2} < 2, 9 > = < 1, \frac{9}{2} >$ $v_B=1/2 <2,9> = <1,9/2>$

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

$v_{B / A} = v_{B} - v_{A} = < 1, \frac{9}{2} > - < \frac{3}{2}, - \frac{7}{2} >$ $v_(B//A) =v_B-v_A= <1,9/2> - <3/2,-7/2>$

$= < (1 - \frac{3}{2}), (\frac{9}{2} + \frac{7}{2}) >$ $= <(1-3/2), (9/2+7/2)>$

$= < - \frac{1}{2}, 8 >$ $= <-1/2, 8>$

Objects A and B are at the origin. If object A moves to (3,−7)(3 ,-7 ) and object B moves to (2,9)(2 ,9 ) over 2s2 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.