# Objects A and B are at the origin. If object A moves to (-6 ,7 ) and object B moves to (-6 ,-1 ) over 3 s, what is the relative velocity of object B from the perspective of object A? Assume that all units are denominated in meters.

Apr 29, 2016

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

#### Explanation:

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

• x-component:
Both the bodies have moved to the same vertical line, namely $x = - 6$ line. Hence their x-components of the velocities are same.

• y-component:
The distance between their final positions is: $\left(7 - \left(- 1\right)\right) = 8 \text{ m}$
Hence the relative velocity along y-axis is: $\frac{8}{3} m {s}^{-} 1$

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

Apr 29, 2016

${v}_{A} = 2 , 67 \text{ m/s}$

#### Explanation:

$\text{displacement=8 meters}$

${v}_{A} = \left(\text{displacement")/("time}\right)$

${v}_{A} = \frac{8}{3}$

${v}_{A} = 2 , 67 \text{ m/s}$

Apr 29, 2016

In 3s displacement of A from (0.0) to (-6,7) $= {\vec{d}}_{A} = \left(- 6 \hat{i} + 7 \hat{j}\right) m$
Velocity of A , ${\vec{V}}_{A} = {\vec{d}}_{A} / 3 = \frac{1}{3} \left(- 6 \hat{i} + 7 \hat{j}\right) \frac{m}{s}$

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