What do you mean by the term relative velocity?

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Relative velocity is the velocity of an object as observed from a specific frame of reference.
Consider two frames of reference,$A$ and $B$,moving with a constant velocity with respect to each other. Let $P$ be a particle.
From the figure,the position vector of particle $P$ with respect to the origin $O$ of frame $A$ is $\vec{r}_{P,A} = \vec{OO'} + \vec{O'P}$.
Since $\vec{OO'} = \vec{r}_{B,A}$ (position of origin $O'$ of frame $B$ w.r.t. origin $O$ of frame $A$) and $\vec{O'P} = \vec{r}_{P,B}$ (position of particle $P$ w.r.t. origin $O'$ of frame $B$),we have:
$\vec{r}_{P,A} = \vec{r}_{P,B} + \vec{r}_{B,A}$
Differentiating this equation with respect to time $t$:
$\frac{d}{dt}(\vec{r}_{P,A}) = \frac{d}{dt}(\vec{r}_{P,B}) + \frac{d}{dt}(\vec{r}_{B,A})$
$\vec{v}_{P,A} = \vec{v}_{P,B} + \vec{v}_{B,A}$
Here,$\vec{v}_{P,A}$ is the velocity of particle $P$ with respect to frame $A$,$\vec{v}_{P,B}$ is the velocity of particle $P$ with respect to frame $B$,and $\vec{v}_{B,A}$ is the velocity of frame $B$ with respect to frame $A$.

Explore More

Similar Questions

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \ km/hr$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be ......... $km/hr$.

Two particles having position vectors $r_1 = (3 \hat{i} + 5 \hat{j}) \text{ m}$ and $r_2 = (-5 \hat{i} - 3 \hat{j}) \text{ m}$ are moving with velocities $v_1 = (4 \hat{i} + 3 \hat{j}) \text{ m/s}$ and $v_2 = (a \hat{i} + 7 \hat{j}) \text{ m/s}$. If they collide after $2 \text{ s}$,then the value of $a$ is:

$A$ passenger train of length $60\, m$ travels at a speed of $80\, km/hr$. Another freight train of length $120\, m$ travels at a speed of $30\, km/hr$. The ratio of times taken by the passenger train to completely cross the freight train when:
$(i)$ they are moving in the same direction,and
$(ii)$ in the opposite directions is

$A$ police van moving on a highway with a speed of $30\; km/h$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192\; km/h.$ If the muzzle speed of the bullet is $150\; m/s,$ with what speed (in $m/s$) does the bullet hit the thief's car?

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be:

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo