**What is Relative Motion?**

Relative motion is basically observing the motion of an object from another object. For example, a person standing on the ground is at rest with respect to ground but he will be in motion with respect to the moon.

The formula for relative velocity as per relative motion is –

Va,b = Va,g − Vb,g |

Where, Va,b = Velocity of a relative to b or the resultant velocity

Va,g = Velocity of a relative to ground

Vb,g = Velocity of b relative to ground

**Example 1- **Now suppose a river is flowing with velocity 4 km/h. So how much time a man will take to cross the river if there is no drift between start and finishing point. Velocity of the man is 5 km/h and width of the river is 600 m.

**Solution –** Let the velocity of the man be x î + y ĵ with respect to river.

Vm = Vm,r + Vr Vm= (x+4) î + y ĵ

As observed from the ground the velocity along x – direction is zero (Since the drift is zero).

So, x = −4km/h —– (1)

Also, x2 + y2 = 25 —– (2)

Using (1) and (2), y = 3 km/h Vm = 3 ĵ

Now considering motion perpendicular to the flow of river, s = 0.6 km v = 3 km/h Therefore time taken to cross the river is, t= 0.2 h

**Example 2**– Another example of relative motion is a man holding umbrella to negotiate rain. When he is standing, he holds the umbrella at an angle 30° with the vertical. When he starts running at 10 km/h the rain appears to fall vertically. We need to find the velocity of rain.

**Solution**– Let the relative motion or relative velocity of rain with respect to ground be x î + y ĵ. Vr,m = (x–10) î + y ĵ

Since the rain appears to fall vertically so the horizontal component will be zero.

Hence, x = 10 km/h —- (1)

Also the rain makes an angle 30° with the vertical so, tan30° = xy —– (2)

Using (1) and (2) we get, y = 10√3 km/h

So the velocity of the rain is, Vr = 10î + 10√3ĵ

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