Objects A and B are at the origin. If object A moves to $(3, - 2)$ $(3 ,-2 )$ and object B moves to $(2, 9)$ $(2 ,9 )$ over $5 s$ $5 s$ , 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 $(3, - 2)$ $(3 ,-2 )$ and object B moves to $(2, 9)$ $(2 ,9 )$ over $5 s$ $5 s$ , 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 · 2016-10-10T13:09:35

Relative velocity of $B$ $B$ with respect to $A$ $A$ is $2.21 m/s$ $2.21 " m/s"$ at an angle of ${95.2}^{\circ}$ $95.2^@$ (relative to the positve X-axis)

Explanation:

After moving $A$ $A$ to $(3, - 2)$ $(3,-2)$ and $B$ $B$ to $(2, 9)$ $(2,9)$
from $A$ $A$ 's perspective $B$ $B$ has moved $< - 1, 11 >$ $<-1,11>$
for a distance of $\sqrt{{(- 1)}^{2} + 11^{2}} = \sqrt{122}$ $sqrt((-1)^2+11^2) = sqrt(122)$
Since this apparent motion takes place over $5$ $5$ seconds
the apparent speed is $\frac{\sqrt{122}}{5} m/s \approx 2.21 m/s$ $sqrt(122)/5 " m/s"~~2.21 " m/s"$

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The angle of this apparent motion, $θ$ $theta$ (relative to the positive X-axis) is such that $tan (θ) = \frac{11}{- 1}$ $tan(theta)=11/(-1)$

$arctan (- \frac{11}{1}) \approx 1.66$ $"arctan(-11/1) ~~1.66$ (radians) $\approx {95.2}^{\circ}$ $~~95.2^@$

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Objects A and B are at the origin. If object A moves to $(3, - 2)$ $(3 ,-2 )$ and object B moves to $(2, 9)$ $(2 ,9 )$ over $5 s$ $5 s$ , 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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Humanities

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Objects A and B are at the origin. If object A moves to (3,−2)(3 ,-2 ) and object B moves to (2,9)(2 ,9 ) over 5s5 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 $(3, - 2)$ $(3 ,-2 )$ and object B moves to $(2, 9)$ $(2 ,9 )$ over $5 s$ $5 s$ , what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.