# Question #3f1d8

May 22, 2016

If a man is standing by the track and train is running at $60$ $k m$/$h r$ to south his relative velocity is $60$ miles south direction.

#### Explanation:

If he is also running at $10$ $k m$/$h r$ towards south, his velocity relative to train is only $60 - 10$ = $50$ $k m$/$h r$ to south.

If he run to north at $10$ $k m$/$h r$ his relative velocity will be $70$ $k m$/$h r$ with train.
Hope this explains the relative velocity.

May 22, 2016

Concept.
For rain problem,
If ${\vec{V}}_{A} \mathmr{and} {\vec{V}}_{B}$ are velocities of objects $A \mathmr{and} B$ respectively then

${\vec{V}}_{A B} = {\vec{V}}_{A} - {\vec{V}}_{B}$ is the velocity of $A$ with respect to $B$.

#### Explanation:

Following the above logic

${\vec{V}}_{r m} = {\vec{V}}_{r} - {\vec{V}}_{m}$ is velocity of rain with respect to man.

See the vector representation on the right side of the figure above.

1. Velocity vectors ${\vec{V}}_{m} \mathmr{and} {\vec{V}}_{r}$ are drawn.
2. Recall $- v e$ sign in front of the the second term.
Therefore, draw $- {\vec{V}}_{m}$ at the tip of ${\vec{V}}_{r}$
3. Join the tail of ${\vec{V}}_{r}$ to the tip of $- {\vec{V}}_{m}$ to obtain ${\vec{V}}_{r m}$ as velocity of rain with respect to man.

Similar steps need to be followed if ${\vec{V}}_{m r}$, velocity of man with respect to rain is to be found.

1. Velocity vectors ${\vec{V}}_{m} \mathmr{and} {\vec{V}}_{r}$ are drawn.
2. We are to find out ${\vec{V}}_{m r}$, velocity of man with respect to rain.
We know that ${\vec{V}}_{m r} = {\vec{V}}_{m} - {\vec{V}}_{r}$
Therefore draw $- {\vec{V}}_{r}$ at the tip of ${\vec{V}}_{m}$
3. Join the tail of ${\vec{V}}_{m}$ to the tip of $- {\vec{V}}_{r}$ to obtain ${\vec{V}}_{m r}$ as velocity of man with respect to rain.