**RELATIVE MOTION **

Relative is a most common word use to compare any property of any object with respect to other object “

X_{AB }= X_{A} ─ X_{B},

↓

X of A with respect to B

Here x may be any physical or non physical quantity

Sign convention

V_{AB }= V_{A} - V_{B}

= + 10 – (16)

V_{AB} = - 6m/s , B says that it seems to be that car A is moving left with 6 m/s

But if V_{BA }= V_{B }- V_{A}

= (16) – (+10)

V_{BA} = 6m/s

A says that if seems to be that car B is moving right with 6 m/s

And if V_{BC} = V_{B}-V_{C}

= (+16) – (-18)

= +34 m/s

C says that it seems to be that car B is moving right with 34 m/s

Also V_{CA} = V_{C} –V_{A}

= - 18 – (+10)

= - 28 m/s

A says that it seems to be that car C is moving left with 28 m/s

**Applications and Understanding of relative motion**

Case : 1 Catching, collision problem

As shown in figure a cop is chasing to a thief . After how long the cop will catch the thief?

**Solution** : First of all we will shift our frame on car so now everything will be relative to car

Initial velocity of car w.r. to bike u_{CB} = u_{C} - u_{B}

= 5 - 2

u_{CB} = 3m/s

Acceleration of car w.r. to bike a_{CB} = a_{C}- a_{B}

= 2 -5

= -3 m/s^{2}

Distance of car w.r. to bike S_{CB} = S_{C} – S_{B}

= 0 – 500

= - 500 mt

Note : Here we are shifting our frame on car so it would be at rest

**Case II:-** Lift or elevator in relative motion.

In this case it is given that boy is dropping a coin inside the lift at the same time lift also start moving down ward with acceleration 5 m/s^{2}, if height of coin from the flower is 10 meter. Then find. Time after which coin strike the floor of lift.

**Solution**: Here again first of all we will shift our frame inside the lift (or on the lift).

So now lift is assume to be at rest now.

Initial velocity of coin w.r. to lift u_{cl} = u_{c} – u_{l}_{ }

Because coins & lift start simultaneously = u – u = 0

Acceleration of coin w.r. to lift a_{cl} = a_{c} – a_{l}

Sign convention = -g -5

= -10 -5

a_{cl}* *= -15m/s^{2}

distance covered by coin w.r to lift h_{cl} = h_{c} –h_{l}

= –10 – 0

= –10 meter

Now

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