Objects A and B are at the origin. If object A moves to $(3, 6)$ $(3 ,6 )$ and object B moves to $(6, - 5)$ $(6 ,-5 )$ over $1 s$ $1 s$ , 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 $(3, 6)$ $(3 ,6 )$ and object B moves to $(6, - 5)$ $(6 ,-5 )$ over $1 s$ $1 s$ , 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 · 2017-07-30T06:42:13

${\to v}_{B w . r . t A} = 3 ˆ i - 11 ˆ j$ $vec v_(B w.r.t A)=3 hat i - 11 hat j$

Explanation:

${\to r}_{i}$ $vec r_i$ = initial displacement vector
${\to r}_{j}$ $vec r_j$ =final displacement vector
${\to r}_{A}$ $vec r_A$ =Displacement vector of A
${\to r}_{B}$ $vec r_B$ =Displacement vector of B
w.r.t=with respect to

${\to r}_{i} = \to 0$ $vec r_i=vec 0$
${\to r}_{f} = 3 ˆ i + 6 ˆ j$ $vec r_f=3hati + 6hatj$
${\to r}_{A} = {\to r}_{f} - {\to r}_{i}$ $vec r_A= vec r_f - vec r_i$
${\to r}_{A} = 3 ˆ i + 6 ˆ j$ $vec r_A=3hati + 6hatj$

${\to r}_{i} = \to 0$ $vec r_i=vec 0$
${\to r}_{f} = 6 ˆ i - 5 ˆ j$ $vec r_f=6hati - 5hatj$
${\to r}_{B} = {\to r}_{f} - {\to r}_{i}$ $vec r_B= vec r_f - vec r_i$
${\to r}_{B} = 6 ˆ i - 5 ˆ j$ $vec r_B=6hati - 5hatj$

${\to r}_{B w . r . t A} = {\to r}_{B} - {\to r}_{A}$ $vec r_(B w.r.t A) = vec r_B - vec r_A$

${\to r}_{B w . r . t A} = 3 ˆ i - 11 ˆ j (m)$ $vec r_(B w.r.t A) = 3hati - 11hatj (m)$

${\to v}_{B w . r . t A} = \frac{{\to r}_{B w . r . t A}}{t}$ $vec v_(B w.r.t A)=(vec r_(B w.r.t A))/t$

${\to v}_{B w . r . t A} = \frac{3 ˆ i - 11 ˆ j (m)}{1 s}$ $vec v_(B w.r.t A)= (3hati - 11hatj (m))/(1s)$

${\to v}_{B w . r . t A} = 3 ˆ i - 11 ˆ j (m \cdot s^{- 1})$ $vec v_(B w.r.t A)= 3hati - 11hatj (m*s^-1)$

$∣ ∣ {\to v}_{B w . r . t A} ∣ ∣ = \sqrt{130} m \cdot s^{- 1}$ $|vec v_(Bw.r.tA)| = sqrt(130) m*s^-1$

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Objects A and B are at the origin. If object A moves to $(3, 6)$ $(3 ,6 )$ and object B moves to $(6, - 5)$ $(6 ,-5 )$ over $1 s$ $1 s$ , 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 (3,6)(3 ,6 ) and object B moves to (6,−5)(6 ,-5 ) over 1s1 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

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Objects A and B are at the origin. If object A moves to $(3, 6)$ $(3 ,6 )$ and object B moves to $(6, - 5)$ $(6 ,-5 )$ over $1 s$ $1 s$ , what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.