Objects A and B are at the origin. If object A moves to $(3, 1)$ $(3 ,1 )$ 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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Objects A and B are at the origin. If object A moves to $(3, 1)$ $(3 ,1 )$ 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 · 2016-07-08T12:55:47

(Using the positive Y-axis as North)
$1.118 \frac{m}{s} at {47.16}^{\circ} W o f N$ $1.118 m/s " at "47.16^@ W of N$

Explanation:

Distance after $8 s$ $8 s$ between A and B
$XXX d = \sqrt{{(3 - 2)}^{2} + {(1 - 4)}^{2}} = \sqrt{10}$ $color(white)("XXX")d=sqrt((3-2)^2+(1-4)^2)=sqrt(10)$ (m)
Speed of B relative to A: $\frac{\sqrt{10}}{8} \frac{m}{s} \approx 1.118 \frac{m}{s}$ $sqrt(10)/8 m/s ~~1.118 m/s$

If $θ$ $theta$ is the angle from A to B (relative to the Y-axis)
then $tan (θ) = \frac{4 - 1}{2 - 3} = - 3$ $tan(theta)=(4-1)/(2-3)=-3$
$\Rightarrow θ \approx {137.16}^{\circ}$ $rArr theta~~137.16^@$ (relative to the positive X-axis)
or
$XXX {47.16}^{\circ}$ $color(white)("XXX")47.16^@$ (relative to the Y-axis)

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

1 Answer

Explanation:

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