Objects A and B are at the origin. If object A moves to $(- 3, - 8)$ $(-3 ,-8 )$ and object B moves to $(- 2, - 1)$ $(-2 ,-1 )$ 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 $(- 3, - 8)$ $(-3 ,-8 )$ and object B moves to $(- 2, - 1)$ $(-2 ,-1 )$ 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 · 2017-10-01T08:33:41

${\to v}_{B A} = \frac{ˆ i + 7 ˆ j}{3} (\frac{m}{s})$ $vecv_(BA)=(hati+7hatj)/3 (m/s)$

Explanation:

A moves $(0, 0)$ $(0,0)$ to $(- 3, - 8)$ $(-3,-8)$ in 3 seconds
Displacement $O A = (- 3 - 0) ˆ i + (- 8 - 0) ˆ j = - 3 ˆ i - 8 ˆ j$ $OA=(-3-0)hati+(-8-0)hatj=-3hati-8hatj$
Velocity of A ${\to v}_{A} = \frac{displacement}{time}$ $vecv_A="displacement"/"time"$
${\to v}_{A} = \frac{- 3 ˆ i - 8 ˆ j}{3}$ $vecv_A=(-3hati-8hatj)/3$

B moves $(0, 0)$ $(0,0)$ to $(- 2, - 1)$ $(-2,-1)$ in 3 seconds
Displacement $O B = (- 2 - 0) ˆ i + (- 1 - 0) ˆ j = - 2 ˆ i - 1 ˆ j$ $OB=(-2-0)hati+(-1-0)hatj=-2hati-1hatj$
Velocity of B ${\to B}_{A} = \frac{displacement}{time}$ $vecB_A="displacement"/"time"$
${\to v}_{B} = \frac{- 2 ˆ i - 1 ˆ j}{3}$ $vecv_B=(-2hati-1hatj)/3$

Velocity of B from perspective of A
${\to v}_{B A} = {\to v}_{B} - {\to v}_{A} = \frac{- 2 ˆ i - 1 ˆ j}{3} - (\frac{- 3 ˆ i - 8 ˆ j}{3})$ $vecv_(BA)=vecv_B-vecv_A=(-2hati-1hatj)/3-((-3hati-8hatj)/3)$
${\to v}_{B A} = \frac{- 2 ˆ i - 1 ˆ j + 3 ˆ i + 8 ˆ j}{3} = \frac{ˆ i + 7 ˆ j}{3} (\frac{m}{s})$ $vecv_(BA)=(-2hati-1hatj+3hati+8hatj)/3=(hati+7hatj)/3 (m/s)$

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Objects A and B are at the origin. If object A moves to $(- 3, - 8)$ $(-3 ,-8 )$ and object B moves to $(- 2, - 1)$ $(-2 ,-1 )$ 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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Explanation:

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Objects A and B are at the origin. If object A moves to (−3,−8)(-3 ,-8 ) and object B moves to (−2,−1)(-2 ,-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.

1 Answer

Explanation:

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Objects A and B are at the origin. If object A moves to $(- 3, - 8)$ $(-3 ,-8 )$ and object B moves to $(- 2, - 1)$ $(-2 ,-1 )$ 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.