Question

An aeroplane flies with a velocity of 450 m/s to the north , while an aeroplaneb travels at a velocity of 500 m/s to the south beside aeroplane a calculate the relative velocity of the aeroplane a with respect to aeroplane b

Answer 1

Velocity : units are m/s . Velocity = displacement / time . displacement = 450km * 1000. displacement = 450,000m . Time = 45*60 = 2,700s . Velocity = 450,000/2,700 . Velocity = 166.7m/s. velocity is a vector quantity and it requires a direction . Because the displacement is 450km. Velocity = 166.7m/s in direction compass heading 85°.

Examples of relative Velocity

We can understand the concept of relative velocity more clearly with the help of the following example.

Example: A plane is traveling at velocity 100 km/hr, in the southward direction. It encounters wind traveling in the west direction at a rate of 25 km/hr. Calculate the resultant velocity of the plane.

Given, the velocity of the wind = Vw = 25km/hr

The velocity of the plane = Va= 100 km/hr

The relative velocity of the plane with respect to the ground can be given as

The angle between the velocity of the wind and that of the plane is 90°. Using the Pythagorean theorem, the resultant velocity can be calculated as,

R2= (100 km/hr)2 + (25 km/hr)2

R2= 10 000 km2/hr2 + 625 km2/hr2

R2= 10 625 km2/hr2

Hence, R = 103.077 km/hr

Answer 2

The relative velocity of aeroplane a with respect to aeroplane b is 950 m/s

Given:

The velocity of plane 'a' moving towards north = 450 m/s

The velocity of plane 'b' moving towards south = 500 m/s

To find:

The relative velocity of aeroplane a with respect to aeroplane b.

Solution:

The velocity of aeroplane 'a' = 450 m/s (North)

The velocity of aeroplane 'b' = 500 m/s (South)

Both the aeroplanes are moving in the opposite direction.

• Relative velocity may be defined as the velocity of an object with respect to another object.

Relative velocity can be calculated:

Va = Velocity of a

Vb = Velocity of b

V ab = Velocity of a with respect to b

V ab = Va - Vb

V ab = 450 - (-500) m/s

V ab = 950 m/s

The relative velocity of aeroplane a with respect to aeroplane b is 950 m/s