Relative Velocity

⁕ Relative Velocity

↪ When two objects A and B are moving with different velocities, then the velocity of one object with respect to another object is called relative velocity.

↪ Here V_AB is the relative velocity of object A w.r.t. B
and V_BA is the relative velocity of object B w.r.t. A

↪ If both the objects are moving in same direction

↪ If the two objects are moving in opposite direction

↪ If the two objects are moving in opposite direction

↪ If the two objects are moving at any angle θ

⁕ Relative Velocity of Rain

↪ If rain is falling vertically with a velocity VR and an observer is moving horizontally with velocity V_M,
↪ then velocity of rain with respect to observer will be,

or,

↪ so in order to save himself from wetting person should hold umbrella at angle θ with vertical. 

⁕ Swimming into the river

↪ A man can swim with velocity V i.e. it is the velocity of man w.r.t. still water.

↪ If water is also flowing velocity V_R then velocity of man relative to ground is,

↪ If the swimming is in the direction of flow of water then

↪ If the swimming is in opposite direction to the flow of water then,

⁕ For Shortest path

↪ If man wants to cross the river such that his displacement should be minimum then is means that he wants to reach just opposite point across the river.

↪ Man should start swimming at an angle θ with the perpendicular to flow of the river.

↪ So that its resultant velocity 
V_M = V + V_R is in the direction of displacement of AB.

↪ To reach at B,

⁕ For minimum time

↪ To cross the river in minimum time the velocity along AB (VCosθ) should be maximum.
↪ It is possible if θ = 0, i.e. swimming should start perpendicular to water current.

↪ Due to effect of river velocity i.e. his displacement will not be minimum but time taken to cross the river will be minimum.

↪ In time t_min swimmer travels distance BC along the river with the speed of river V_R.

↪ Distance travelled along river flow = drift of man = t_min V_R