Mayank give a situation to his student that there are four particles A, B, C and D and their relative velocities are given as V_DC = 20 m/s toward the north, V_BC = 20 m/s towards the east and V_BA = 20 m/s towards the south. Then V_DA is?

Question

Question

Answer 1

CONCEPT:

Relative Velocity: Relative velocity is defined as the velocity of one object with respect to another.
It is represented by V_AB means the velocity of A with respect to B
It is represented by VBA means the velocity of B with respect to A

|V_AB| = |V_BA|

VAB = -VBA

Relative motion in two dimensions is the same as in the case of one dimension.
In relative motion in two-dimensional use the following sign to represent a different direction
East = î
West = -î
North = ĵ
South = -ĵ

CALCULATION:

Given:

VDC = 20 m/s toward the north; VBC = 20 m/s towards the east; VBA = 20 m/s towards the south

Let us consider direction according to the cartesian system that is

We know that

V_DC = V_D - V_C

VD - VC = 20ĵ ---(i)

V_BC = V_B - V_C

V_B - V_C = 20î ---(ii)

V_BA = V_B - V_A

V_B - V_A = -20ĵ ---(iii)

By subtracting eq(ii) from eq (i) we get

V_D - V_B = 20ĵ - 20î ---(iv)

By adding eq(iii) and eq(iv) we get

V_D - V_A = -20î

V_DA = 20 m/s towards west

Hence option 1 is correct

Mistake Points

While solving relative motion in two dimensions always use the vector notification to avoid mistakes.