Objects A and B are at the origin. If object A moves to $(- 5, 2)$ $(-5 ,2 )$ and object B moves to $(- 1, - 8)$ $(-1 ,-8 )$ over $4 s$ $4 s$ , what is the relative velocity of object B from the perspective of object A?

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Objects A and B are at the origin. If object A moves to $(- 5, 2)$ $(-5 ,2 )$ and object B moves to $(- 1, - 8)$ $(-1 ,-8 )$ over $4 s$ $4 s$ , what is the relative velocity of object B from the perspective of object A?

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Answer 1 · 2017-03-24T11:28:31

Relative velocity (approximately): $2.7$ $color(green)(2.7)$ units/sec at an angle of $- {68.2}^{\circ}$ $color(green)(-68.2^@)$

Explanation:

Here is a graph of the resultant positions:
enter image source here

The relative displacement of $B$ $B$ with respect to $A$ $A$ is
$XXX 4 units horizontally$ $color(white)("XXX")4 " units horizontally"$ and
$XXX - 10 units vertically$ $color(white)("XXX")-10 " units vertically"$ .

The angle of displacement (to $B$ $B$ relative to $A$ $A$ ) is therefore
$XXX arctan (\frac{- 10}{4}) \approx - 1.19028995 (radians) \approx - {68.19859051}^{\circ}$ $color(white)("XXX")arctan((-10)/4)~~-1.19028995" (radians)" ~~-68.19859051^@$
(calculator used for this)

The distance from $A$ $A$ to $B$ $B$ (using the Pythagorean Theorem) is
$XXX \sqrt{4^{2} + {(- 10)}^{2}} = \sqrt{116} = 2 \sqrt{29} units$ $color(white)("XXX")sqrt(4^2+(-10)^2)=sqrt(116)=2sqrt(29)" units"$

Since this distance was covered over a period of $4$ $4$ sec.
the average speed must be $(2sqrt(29))/4 " units/sec" ~~2.69258..." units/sec."$

velocity is a combination of speed and angle.

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Objects A and B are at the origin. If object A moves to $(- 5, 2)$ $(-5 ,2 )$ and object B moves to $(- 1, - 8)$ $(-1 ,-8 )$ over $4 s$ $4 s$ , what is the relative velocity of object B from the perspective of object A?

1 Answer

Explanation:

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Objects A and B are at the origin. If object A moves to (-5 ,2 )(−5,2)(-5 ,2 ) and object B moves to (-1 ,-8 )(−1,−8)(-1 ,-8 ) over 4 s4s4 s, what is the relative velocity of object B from the perspective of object A?

1 Answer

Explanation:

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Objects A and B are at the origin. If object A moves to $(- 5, 2)$ $(-5 ,2 )$ and object B moves to $(- 1, - 8)$ $(-1 ,-8 )$ over $4 s$ $4 s$ , what is the relative velocity of object B from the perspective of object A?