Objects A and B are at the origin. If object A moves to $(5, - 1)$ $(5 ,-1 )$ and object B moves to $(- 8, 1)$ $(-8 ,1 )$ 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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Objects A and B are at the origin. If object A moves to $(5, - 1)$ $(5 ,-1 )$ and object B moves to $(- 8, 1)$ $(-8 ,1 )$ 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 · 2016-04-26T11:14:58

Treating the positive X-axis as North,
$XXX approximately 4.38 \frac{m}{sec} at {8.75}^{\circ} N of W$ $color(white)("XXX")"approximately "4.38 m/(sec)" at "8.75^@ N" of "W$

Explanation:

The distance between points A and B has increased from $0$ $0$ meters to
$XXX \sqrt{{(5 - (- 8))}^{2} + {(1 - (- 1))}^{2}} = \sqrt{173} \approx 13.15$ $color(white)("XXX")sqrt((5-(-8))^2+(1-(-1))^2)=sqrt(173)~~13.15$ meters
for an average speed of
$XXX \frac{\sqrt{173} m}{3 sec} \approx 4.38 \frac{m}{sec}$ $color(white)("XXX")(sqrt(173) m)/(3 sec) ~~4.38 (m)/(sec)$

Relative to A, B has moved $13$ $13$ meters East and $2$ $2$ meters North.
If $θ$ $theta$ is the angle North of due East for B's movement relative to A then
$XXX tan (θ) = \frac{2}{13}$ $color(white)("XXX")tan(theta)=2/13$

$XXX \Rightarrow θ = arctan (\frac{2}{13}) \approx {8.75}^{\circ}$ $color(white)("XXX")rArr theta = arctan(2/13)~~8.75^@$

(Remember that velocity must always include a direction as well as a speed).

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Objects A and B are at the origin. If object A moves to $(5, - 1)$ $(5 ,-1 )$ and object B moves to $(- 8, 1)$ $(-8 ,1 )$ 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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Objects A and B are at the origin. If object A moves to (5,−1)(5 ,-1 ) and object B moves to (−8,1)(-8 ,1 ) 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.

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Objects A and B are at the origin. If object A moves to $(5, - 1)$ $(5 ,-1 )$ and object B moves to $(- 8, 1)$ $(-8 ,1 )$ 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.