Objects A and B are at the origin. If object A moves to $(- 6, 7)$ $(-6 ,7 )$ and object B moves to $(- 6, - 1)$ $(-6 ,-1 )$ 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 $(- 6, 7)$ $(-6 ,7 )$ and object B moves to $(- 6, - 1)$ $(-6 ,-1 )$ 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 · 2016-04-29T10:54:08

$\frac{8}{3} m s^{- 1}$ $8/3ms^-1$

Explanation:

Relative velocity is a vector quantity. Lets check component wise:

x-component:
Both the bodies have moved to the same vertical line, namely $x = - 6$ $x= -6$ line. Hence their x-components of the velocities are same.
y-component:
The distance between their final positions is: $(7 - (- 1)) = 8 m$ $(7-(-1)) = 8" m"$
Hence the relative velocity along y-axis is: $\frac{8}{3} m s^{- 1}$ $8/3 ms^-1$

Hence the relative velocity is $\frac{8}{3} m s^{- 1}$ $8/3 ms^-1$ along y-axis.

Answer 2 · 2016-04-29T11:18:44

$v_{A} = 2, 67 m/s$ $v_A=2,67 " m/s"$

Explanation:

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$displacement=8 meters$ $"displacement=8 meters"$

$v_{A} = \frac{displacement}{time}$ $v_A=("displacement")/("time")$

$v_{A} = \frac{8}{3}$ $v_A=8/3$

$v_{A} = 2, 67 m/s$ $v_A=2,67 " m/s"$

Answer 3 · 2016-04-29T18:49:03

In 3s displacement of A from (0.0) to (-6,7) $= {\to d}_{A} = (- 6 ˆ i + 7 ˆ j) m$ $=vecd_A=(-6hati+7hatj)m$
Velocity of A , ${\to V}_{A} = \frac{{\to d}_{A}}{3} = \frac{1}{3} (- 6 ˆ i + 7 ˆ j) \frac{m}{s}$ $vecV_A=vecd_A/3=1/3(-6hati+7hatj)m/s$

In 3s displacement of B from (0.0) to (-6,-1) $= {\to d}_{B} = (- 6 ˆ i - ˆ j) m$ $=vecd_B=(-6hati-hatj)m$
Velocity of B, ${\to V}_{B} = \frac{{\to d}_{B}}{3} = \frac{1}{3} (- 6 ˆ i - ˆ j) \frac{m}{s}$ $vecV_B=vecd_B/3=1/3(-6hati-hatj)m/s$
The relative velocity of object B from the perspective of object A
is ${\to V}_{B} - {\to V}_{A} = \frac{1}{3} (- 6 ˆ i - ˆ j + 6 ˆ i - 7 ˆ j) = - \frac{8}{3} ˆ j \frac{m}{s}$ $vecV_B-vecV_A=1/3(-6hati-hatj+6hati-7hatj)=-8/3hatjm/s$
So magnitude of relative velocity is $\frac{8}{3} \frac{m}{s}$ $8/3m/s$ and it is directed towards negative direction of y-axis i.e. $270^{o}$ $270^o$ with positive direction of X-axis

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Objects A and B are at the origin. If object A moves to $(- 6, 7)$ $(-6 ,7 )$ and object B moves to $(- 6, - 1)$ $(-6 ,-1 )$ 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 (−6,7)(-6 ,7 ) and object B moves to (−6,−1)(-6 ,-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.

3 Answers

Explanation:

Explanation:

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Objects A and B are at the origin. If object A moves to $(- 6, 7)$ $(-6 ,7 )$ and object B moves to $(- 6, - 1)$ $(-6 ,-1 )$ 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.