Objects A and B are at the origin. If object A moves to $(4, - 2)$ $(4 ,-2 )$ and object B moves to $(2, 4)$ $(2 ,4 )$ over $8 s$ $8 s$ , 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 · 2017-09-03T06:36:13

The relatve velocity is $= < \frac{1}{4}, - \frac{3}{4} >$ $= <1/4, -3/4>$ ms^-1

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The absolute velocity of $A$ $A$ is $v_{A} = \frac{1}{8} < 4, - 2 > = < \frac{1}{2}, - \frac{1}{4} >$ $v_A=1/8 <4,-2> = <1/2,-1/4>$

The absolute velocity of $B$ $B$ is $v_{B} = \frac{1}{8} < 2, 4 > = < \frac{1}{4}, \frac{1}{2} >$ $v_B=1/8 <2,4> = <1/4,1/2>$

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

$v_{B / A} = v_{B} - v_{A} = < \frac{1}{2}, - \frac{1}{4} > - < \frac{1}{4}, \frac{1}{2} >$ $v_(B//A) =v_B-v_A= <1/2,-1/4> - <1/4,1/2>$

$= < (\frac{1}{2} - \frac{1}{4}), (- \frac{1}{4} - \frac{1}{2}) >$ $= <(1/2-1/4), (-1/4-1/2)>$

$= < \frac{1}{4}, - \frac{3}{4} >$ $= <1/4, -3/4>$

Objects A and B are at the origin. If object A moves to (4,−2)(4 ,-2 ) and object B moves to (2,4)(2 ,4 ) over 8s8 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.