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

In summary, the swimmer's absolute speed is 2.5 m/s at a 45 degree angle to the current. This means that the swimmer's speed is split into two equal components, one across the river and one down the river. The swimmer's speed relative to the current is the sum of these two components.
  • #1
bionut
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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?
 
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  • #2
bionut said:
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 45o 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.
 

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

What is relative motion of a swimmer?

Relative motion of a swimmer is the concept of how an observer perceives the movement of a swimmer in relation to their own motion or frame of reference. It takes into account the swimmer's speed, direction, and position relative to the observer's perspective.

How does relative motion affect a swimmer's performance?

Relative motion can have a significant impact on a swimmer's performance. For example, if the swimmer is swimming against a current, their speed and efficiency will be affected. Similarly, if the swimmer is swimming in a lane next to a faster swimmer, they may feel a stronger current and have to adjust their technique accordingly.

What factors influence relative motion in swimming?

The main factors that can influence relative motion in swimming are the swimmer's speed, direction, and position, as well as external factors such as current, wind, and other swimmers in the same lane. The shape and size of the pool or body of water can also affect relative motion.

How can understanding relative motion help with race strategy?

Understanding relative motion can help swimmers develop a more effective race strategy. By taking into account their speed and position in relation to their competitors, swimmers can make strategic decisions such as when to make a move to overtake another swimmer or how to conserve energy by swimming in a certain position in the lane.

What are some common techniques used to minimize the effects of relative motion in swimming?

Swimmers may use various techniques to minimize the effects of relative motion, such as drafting behind another swimmer to reduce drag and conserve energy. They may also adjust their stroke technique or breathing pattern to compensate for currents or other external factors. Pool design, such as incorporating lane dividers and wave-reducing technology, can also help to minimize the effects of relative motion on swimmers.

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