How Do You Calculate the Swimmer's Velocity Relative to the Current?

[bionut]

A swimmer crossing a river proceeds at an absolute speed of 2.5 m/s on a course oriented at a 45degree angle to the 1 m/s current. Given that the absolute velocity of the swimmer is equal to the vector sum of the velocity of the current and the velocity of the swimmer with respect to the current what is the magnitude and direction of the velcoity of the swimmer with respect to the current?


So:
1. absolute speed = resulatant = 2.5 m/s
2. Known:
Vc = 1 m/s -->
Vs = 2.5 m/s @ 45 degree angle

Vs= Vc + Vs/Vc

Im stuck with how I work out the Velocity of the swimmer in respect to the velcoity of the current.
I tried using R2=a2 + b2 but they didnt work any suggestion where to start?

 

[PeterO]

A swimmer crossing a river proceeds at an absolute speed of 2.5 m/s on a course oriented at a 45degree angle to the 1 m/s current. Given that the absolute velocity of the swimmer is equal to the vector sum of the velocity of the current and the velocity of the swimmer with respect to the current what is the magnitude and direction of the velcoity of the swimmer with respect to the current?So:
1. absolute speed = resulatant = 2.5 m/s
2. Known:
Vc = 1 m/s -->
Vs = 2.5 m/s @ 45 degree angle

Vs= Vc + Vs/Vc

Im stuck with how I work out the Velocity of the swimmer in respect to the velcoity of the current.
I tried using R2=a2 + b2 but they didnt work any suggestion where to start?

Is there any indication of whether the swimmer's motion is angled down-stream or upstream? I suspect down-stream, as the current is down stream so saying 45 degrees relative to the current at least half implies the swimmer is also angled down stream.

If the absolute speed is 2.5, angled at 45^o to the current, then the absolute speed has equal components across the river and down the river.

The component across the river is entirely due to the swimmer.
The component down the river is partially due to the swimmer and partially due to the current.

The swimmers speed relative to the river [the current] is just the sum of the two smimmer's parts.