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Relative Velocity MCQ - Practice Questions with Answers

Edited By admin | Updated on Sep 25, 2023 25:23 PM | #NEET

Quick Facts

Relative Velocity is considered one of the most asked concept.
23 Questions around this concept.

Solve by difficulty

A bus is moving at a speed of 10ms^-1 on a straight road. A scooterist wishes to overtake the bus in 100s. If the bus is at a distance of 1km from the scooterist, with what speed should the scooterist chase the bus?

40 ms^-1

25 ms^-1

10 ms^-1

20 ms^-1

View Solution

Ship A is moving west at a speed of $10\ km\ h^{-1}$ , and ship B is moving north at a speed of $100\ km$ south of A. The time at which the distance between them becomes shortest is:

$0\ h$

$5\ h$

$5\sqrt2\ h\$

$10\sqrt2\ h\$

View Solution

Concepts Covered - 1

Relative Velocity

Relative change in position of one object with respect to another object.
Formula-

Relative velocity of object A with respect to object B .

$\vec{V}_{AB}= \vec{V}_A-\vec{V}_B$

Case of Relative velocity

When A and B are moving along a straight line in the same direction.

$\underset{V_A}{\rightarrow}$ = Velocity of object A.

$\underset{V_B}{\rightarrow}$ = Velocity of object B.

Then, relative velocity of A w.r.t B is

$\vec{V}_{AB}=\vec{V}_{A}-\vec{V}_{B}$

$\vec{V}_{AB},\vec{V}_{A},\vec{V}_{B}$ all are in same direction. (If $\vec{V}_{A}> \vec{V}_{B}$ )

And Relative velocity of B w.r.t A is

$\vec{V}_{BA}=\vec{V}_{B}-\vec{V}_{A}$

& $\vec{V}_{AB}=-\vec{V}_{BA}$

When A & B are moving along with straight line in opposite direction.

Relative velocity of A with respect to B is.

$\vec{V}_{AB}=\vec{V}_{A}-(-\vec{V}_{B})$

$\vec{V}_{AB}=\vec{V}_{A}+(\vec{V}_{B})$

3. Relative Velocity when bodies moving at an angle to each other

Relative velocity of a body, A with respected body B

$V_{AB}= \sqrt{V_{A}^{2}+V_{B}^{2}+2V_{A}V_{B}\cos \left ( 180-\theta \right )}$

$= \sqrt{V_{A}^{2}+V_{B}^{2}-2V_{A}V_{B}\cos \left ( \theta \right )}$

Where, $\\*V_{A}= velocity\: of\: A\\* V_{B}= velocity\: of\: B\\* \Theta = angle \: between \: A \: and \: B$

If $\overrightarrow{V_{AB}}$ makes an angle $\beta$ with the direction of $\overrightarrow{V_{A}}$ , then

$\\*\tan \beta = \frac{V_{B}\sin \left ( 180-\Theta \right )}{V_{A}+V_{B}\cos \left ( 180-\Theta \right ) }\\*\\* = \frac{V_{B}\cdot \sin\Theta }{V_{A}-V_{B}\cos \Theta }$