According to relative velocity formula we know that when two bodies move towards each other the relative velocity is equal to the sum of two velocities. Then why in calculating upstream where the direction of velocity of stream is against the direction of velocity of boat in still water we subtract the former from the latter even when they are opposite to each other?

### Asked by ahanaganguly55 | 28th May, 2021, 03:59: PM

### When two bodies A and B are moving towards each other , distance between them decreasing with respect to time.
Let u_{A} be the velocity of A that move towards B . Let u_{B} be the velocity of B that moves towards A .
In a time interval Δt , distance moved by A towards B is ( u_{A} × Δt ) .
In same time interal Δt , distance moved by B towards A is ( u_{B} × Δt ) .
Hence decrease of distance between A and B in this time interval is ( u_{A} + u_{B }) Δt .
Hence with respect to body-A , body-B moves towards body-A with speed ( u_{A} + u_{B }) .
Similarly, with respect to body-B , body-A moves towards body-B with speed ( u_{A} + u_{B }) .
When two bodies A and B are moving towards each other , relative velocity one body with respect to other is sum of their individual velocities.
------------------------------------------------
In above scenario , two bodies are not in contact. But when a body travels in upstream , travelling body and stream are in contact.
Let the body moves with velocity u and stream velocity be v in opposite direction.
In a time interval Δt, if the body moves towards upstream direction , then distance moved by body is ( u Δt ) .
But in this same time interval, stream has moved the body to a distance ( v Δt ) in opposite direction .
Hence net displacement by the body equlas [ ( u - v ) Δt ]
Hence to get the net velocity of moving body in upstream , we need to subtract the stream velocity from the velocity of moving body.

_{A}be the velocity of A that move towards B . Let u

_{B}be the velocity of B that moves towards A .

_{A}× Δt ) .

_{B}× Δt ) .

_{A}+ u

_{B }) Δt .

_{A}+ u

_{B }) .

_{A}+ u

_{B }) .

### Answered by Thiyagarajan K | 28th May, 2021, 05:20: PM

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