Objects A and B are at the origin. If object A moves to $(- 6, - 5)$ $(-6 ,-5 )$ and object B moves to $(- 1, 12)$ $(-1 ,12 )$ 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 $(- 6, - 5)$ $(-6 ,-5 )$ and object B moves to $(- 1, 12)$ $(-1 ,12 )$ 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 · 2017-09-27T17:34:19

${\to v}_{B A} = (\frac{5}{3} ˆ i + \frac{17}{3} ˆ j) \frac{m}{s}$ $vecv_(BA)=(5/3hati+17/3hatj) m/s$

Explanation:

A moves Origin $(0, 0)$ $(0,0)$ to $(- 6, - 5)$ $(-6,-5)$
Displacement vector of A is
${\to d}_{A} = (- 6 - 0) ˆ i + (- 5 - 0) ˆ j$ $vecd_A=(-6-0)hati+(-5-0)hatj$
${\to d}_{A} = - 6 ˆ i - 5 ˆ j$ $vecd_A=-6hati-5hatj$
time is 3 sec
Velocity vector of A
${\to v}_{A} = \frac{{\to d}_{A}}{t} = \frac{- 6 ˆ i - 5 ˆ j}{3} = - \frac{6}{3} ˆ i - \frac{5}{3} ˆ j$ $vecv_A=vecd_A/t=(-6hati-5hatj)/3=-6/3hati-5/3hatj$

B moves Origin $(0, 0)$ $(0,0)$ to $(- 1, 12)$ $(-1,12)$
Displacement vector of B is
${\to d}_{B} = (- 1 - 0) ˆ i + (12 - 0) ˆ j$ $vecd_B=(-1-0)hati+(12-0)hatj$
${\to d}_{B} = - 1 ˆ i + 12 ˆ j$ $vecd_B=-1hati+12hatj$
time is 3 sec
Velocity vector of B
${\to v}_{B} = \frac{{\to d}_{B}}{t} = \frac{- 1 ˆ i + 12 ˆ j}{3} = - \frac{1}{3} ˆ i + \frac{12}{3} ˆ j$ $vecv_B=vecd_B/t=(-1hati+12hatj)/3=-1/3hati+12/3hatj$

Relative Velocity of B from the perspective of A
${\to v}_{B A} = {\to v}_{B} - {\to v}_{A}$ $vecv_(BA)=vecv_B-vecv_A$
${\to v}_{B A} = \frac{- 1 ˆ i + 12 ˆ j}{3} - \frac{- 6 ˆ i - 5 ˆ j}{3}$ $vecv_(BA)=(-1hati+12hatj)/3-(-6hati-5hatj)/3$
${\to v}_{B A} = \frac{- 1 ˆ i + 12 ˆ j - (- 6 ˆ i - 5 ˆ j)}{3}$ $vecv_(BA)=(-1hati+12hatj-(-6hati-5hatj))/3$
${\to v}_{B A} = \frac{- 1 ˆ i + 12 ˆ j + 6 ˆ i + 5 ˆ j}{3}$ $vecv_(BA)=(-1hati+12hatj+6hati+5hatj)/3$
${\to v}_{B A} = \frac{5 ˆ i + 17 ˆ j}{3} = (\frac{5}{3} ˆ i + \frac{17}{3} ˆ j) (\frac{m}{s})$ $vecv_(BA)=(5hati+17hatj)/3=(5/3hati+17/3hatj) (m/s)$

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Objects A and B are at the origin. If object A moves to $(- 6, - 5)$ $(-6 ,-5 )$ and object B moves to $(- 1, 12)$ $(-1 ,12 )$ 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 (−6,−5)(-6 ,-5 ) and object B moves to (−1,12)(-1 ,12 ) 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 $(- 6, - 5)$ $(-6 ,-5 )$ and object B moves to $(- 1, 12)$ $(-1 ,12 )$ 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.