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Relative Velocity - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Relative Velocity is considered one of the most asked concept.

  • 19 Questions around this concept.

Solve by difficulty

A  particle of mass m  is at rest at the origin at time  t=0. It is subjected to a force F\left ( t \right )= F_{0}e^{-bt} in the x direction .Its speed v(t) is depicted by which of the following curves ?

A police jeep chased a thief at  45\frac{km}{h}, while thief traveled at  153\ \frac{km}{hr}. The police fired a bullet with an initial speed of   180\ \frac{m}{s}. The speed at which it hits the thief’s car is:

Concepts Covered - 1

Relative Velocity
  • Rate of change in position of one object with respect to another object with time is defined as relative velocity of one object with another.

  • Formula-

           Relative  velocity of object A with respect to object B .

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

  •  Relative velocity of A with respect to B is velocity of A as observed by B.
  • Case of Relative velocity

  1. 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}

  1. 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}

                                       {V}_{AB}=V_{A}+V_{B}

       3. Relative Velocity when bodies moving at an angle \theta 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 }

  • If two bodies are moving at right angles to each other.

           Relative Velocity of A with respect to B is

                                   V_{AB}=\sqrt{{V_{A}}^{2}+{V_{B}}^{2}}

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Relative Velocity

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