Relative velocity of a swimmer

In summary, the river current is 22 m/s [South], the width of the river is 325m, and the speed of the person swimming is 47 m/s. To determine how far up or down the stream the person will end up, we first find the vector sum of the current and the swimmer's speed. This creates a triangle with sides of 47, 22, and an angle of 97.5 degrees. Solving for the hypotenuse using the cosine law gives a magnitude of 54.433. Next, we use the same equation to find the angle formed by the hypotenuse and the swimmer, which is 23.622 degrees. Adding this to the swimmer's
  • #1
thegame
32
0
river current = 22 m/s [South]
width of the river from one side to the other = 325m
speed of person swiming = 47 m/s



if the person travels 47 m/s [E 7.5 degrees S] then how far up or down the stream will he end up when he reaches the other side?
 
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  • #2
alright! i just did a ton of these!

first, find the vector V(current)+V(swimmer)
if you draw it, you get a triange with one leg 47, another 22, and the angle between them 97.5

then solve for the hypotnuse (c^2=a^2+b^2-2ab cos C), which gives you the magnitude of 54.433

use the same equation to get the angle formed by the hypotnuse and the swimmer. this is 23.622 degrees.

since the swimmer is at a 7.5 degree angle, add this to 23.622,
31.122

now you draw the river. from one side to the other is 325 m. now draw a line [E 31.122 S] and use inverse tan to get the answer,
196 m down

someone may want to double check. i might have done something stupid, or even did it wrong all together. haha.
 
  • #3
After trying it a few times, I got 196m too..
 

What is relative velocity?

Relative velocity refers to the velocity of an object or person in relation to another moving object or frame of reference. It takes into account both the individual's own velocity and the velocity of the reference point.

How does relative velocity apply to swimmers?

In swimming, relative velocity is used to measure the speed of a swimmer in relation to the moving water around them. It takes into account factors such as the current, wind, and waves, which can affect the swimmer's speed.

What is the formula for calculating relative velocity in swimming?

The formula for relative velocity in swimming is: Vrel = Vswimmer - Vwater, where Vrel is the relative velocity, Vswimmer is the swimmer's velocity, and Vwater is the velocity of the water.

How does relative velocity affect a swimmer's performance?

Relative velocity can greatly impact a swimmer's performance, as it determines the speed at which they are able to move through the water. Swimmers must be aware of their relative velocity and adjust their technique accordingly to optimize their performance.

What are some strategies for maximizing relative velocity in swimming?

To maximize relative velocity in swimming, swimmers can adjust their body position, streamline their movements, and use proper breathing techniques. They can also take advantage of the current and waves to propel themselves forward.

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