What do you mean by term relative velocity ?
What do you mean by term relative velocity ?
As shown in the figure $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ are two frames of reference moving with constant velocity w.r.t. to each other. These frames are called inertial reference frames.
If an observer is in $\mathrm{S}_{1}$ and other observer in $\mathrm{S}_{2}$ observes the motion of particle $\mathrm{P}$, then following observation can be used.
Consider the position of particle P from the origin O of S $_{1}$ be given by $\vec{r}_{\mathrm{PS}_{1}}=\overrightarrow{\mathrm{OP}}$ and the position vector of particle $\mathrm{P}$ from $\mathrm{O}^{\prime}$ of $\mathrm{S}_{2}$ is given by $\vec{r}_{\mathrm{P} \mathrm{S}_{2}}=\overrightarrow{\mathrm{O}^{\prime} \mathrm{P}}$. The position vector of origin $\mathrm{O}^{\prime}$ of $\mathrm{S}_{2}$ w.r.t.
$\mathrm{O}$ if $\mathrm{S}_{1}$ is given by $\vec{r}_{\mathrm{S}_{2}, \mathrm{~S}_{1}}=\overrightarrow{\mathrm{OO}}^{\prime}$
Then from the figure,
$\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{OO}^{\prime}}+\overrightarrow{\mathrm{OP}}=\overrightarrow{\mathrm{OP}}+\overrightarrow{\mathrm{OO}^{\prime}}$ $\therefore \vec{r}_{\mathrm{PSS}_{1}}=\vec{r}_{\mathrm{P}, \mathrm{s}_{2}}+\vec{r} \mathrm{~s}_{2}, \mathrm{~s}_{1}$ Differentiating equation (1) w.r.t. time, we get
$\frac{d}{d t}\left(\vec{r} \mathrm{P}, \mathrm{s}_{1}\right)=\frac{d}{d t}\left(\vec{r} \mathrm{P}, \mathrm{s}_{2}\right)+\frac{d}{d t}\left(\rightarrow \overrightarrow{\mathrm{s}}_{2}, \mathrm{~s}_{1}\right)$
$\therefore \overrightarrow{\mathrm{V}} \mathrm{P}, \mathrm{s}_{1}=\overrightarrow{\mathrm{V}} \mathrm{P}, \mathrm{s}_{2}+\overrightarrow{\mathrm{V}} \mathrm{s}_{2}, \mathrm{~s}_{1}$
Here, $\vec{V}_{\mathrm{P}, \mathrm{S}_{1}}$ is the velocity of the particle w.r.t. reference frame $\mathrm{S}_{1}$,
$\vec{V} \mathrm{P}_{1} \mathrm{~S}_{2}$ is the velocity of the particle w.r.t. reference frame $\mathrm{S}_{2}$ and
$\vec{V} \mathrm{~s}_{2}, \mathrm{~s}_{1}$ is the velocity of reference frame $\mathrm{S}_{2}$ w.r.t. frame $\mathrm{S}_{1}$
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