If you look outside the home window of a relocating train, you will observe that one more train lie stationary appears to be moving in a behind direction. How does a stationary train seem to move? Behind it, there lies a really important ide of loved one motion, which will certainly make us understand why objects appear to move differently with various frames.

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What is loved one Motion?

The principle of reference frames was an initial introduced to discuss relative activity in one or much more dimensions. When we say an object has a details velocity, climate this velocity is with respect to some structure that is well-known as the referral frame. In day-to-day life, once we measure up the velocity of an object, the reference frame is required to be the soil or the earth.

For example, if you room travelling in a train and the train is relocating at a speed of 100 km/hr, then your speed according to an additional passenger sitting on that train is zero. According to him, you room not moving. However if someone observes friend from outside the train, standing on the ground, follow to him, friend are moving with 100 km/hr as you room on the train and also the train is moving with 100 km/hr.

Here, the motion observed through the observer depends on the ar (frame) of the observer. This kind of motion is dubbed relative motion.

Relative Velocity

The family member velocity of things A with respect to object B is the rate of change of place of the thing A through respect to object B.

If VA and VB be the velocities that objects A and also B through respect come the ground, then

The family member velocity the A with respect to B is VAB = VA – VB

The loved one velocity that B v respect to A is VBA = VB – VA

Relative motion in One Dimension

In one-dimensional motion, objects move in a directly line. So over there are just two possible cases:

Objects are moving in the same directionObjects are relocating in opposing direction

Again take the instance of a man sitting on the train if the train is relocating with 100 km/hr forward. Climate according come the man sitting on the train, the trees external are moving backwards v 100 km/hr.

Because from the man’s point of view, the outside atmosphere is moving in the opposite direction come the train through the very same velocity.

So because that all types of questions, if you have to discover the velocity of A through respect to B, then assume the B is at rest and also give the velocity that B to A in the contrary direction.

Relative movement in 2 Dimensions

The same concept will be applicable in two-dimensional motion. If you have to find the velocity of A through respect come B, assume the B is in ~ rest and give the velocity of B come A in the opposite direction.

Let us think about two objects A and B i m sorry are relocating with velocities Va and also Vb through respect to some usual frame of reference, say, through respect come the soil or the earth. We have to uncover the velocity of A v respect to B, therefore assume the B is at rest and also give the velocity the B to A in the opposite direction.

Vab = va – vb

Similarly, because that the velocity of thing B with respect to A, assume that A is in ~ rest and also give the velocity of A to B in the opposite direction.

Vba = vb – va

Relative activity Problems

1) Two body A and also B room travelling v the same speed 100 km/hr in opposite directions. Uncover the loved one velocity of human body A v respect to body B and also relative velocity of body B through respect to human body A.

The family member velocity the A w.r.t. B is VAB = VA – VB

= 100- (-100)

= 200 km/hr

Relative velocity of B w.r.t. A is VBA = VB – VA

= -100 – (100)

= -200 km/hr (-ve means towards left)

In the very same question, if both body are relocating in the same direction through the exact same speed then,

The family member velocity that A with respect come B is VAB = VA – VB

= 100-100

= 0

The relative velocity of B through respect to A is VBA = VB – VA

= 100-100

= 0

That method A is at rest with respect come B and also B is at rest with respect come A, yet both are moving with 100 km/hr with respect to the ground.

2) discover the loved one velocity of rain v respect come the moving man:

Here the guy is walking towards the west through velocity Vm⃗\vecV_mVm​​and the rain is fall vertically downward through velocity Vr⃗\vecV_rVr​​

So, the loved one velocity the rain w.r.t. Guy is Vm⃗=Vr⃗\vecV_m=\vecV_rVm​​=Vr​​

We know that the magnitude of the vector distinction is provided by,

Vrm=Vr2+Vm2+2VrVmcos900=Vr2+Vm2Vrm =\sqrtV_r^2+V_m^2+2V_rV_mcos90^0= \sqrtV_r^2+V_m^2Vrm=Vr2​+Vm2​+2Vr​Vm​cos900

​=Vr2​+Vm2​​(from the diagram, Vm‾\overlineVmVm is the hypotenuse the the triangle.

It θ is the angle which  Vrm‾\overlineVrmVrm provides with the upright direction then,

tan θ = BD/OB = Vm / Vr

In the above case, if the man wants to safeguard himself from the rain, that should organize his umbrella in the direction of the loved one velocity of rain with respect come the man. I.e.the umbrella have to be hosted making an angle θ ( θ=tan−1VmVr\theta =tan^-1\fracV_mV_rθ=tan−1Vr​Vm​​) west the vertical.

is the angle of the umbrella native the vertical.

3) Boat and river problem. Discover the velocity the the boat with respect come the river.

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Here the velocity that the watercraft with respect to the water or the velocity the the boat in tho water is given. If the observer is observing the movement from the ground, then the velocity of the boat with respect come the soil is same to the velocity the the boat in still water plus the velocity that the water.

i.e Velocity that a boat with respect come the ground = velocity the the boat in still water + velocity of the water v respect to the ground