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Suppose that you are swimming in a river while a friend watches from the shore. In calm water, you swim at a speed of 1.25 m/s . The river has a current that runs at a speed of 1.00 m/s . Which of the following gives the correct components for the current velocity and the pure swimming velocity (i.e., the velocity that you would have in still water) using this coordinate system?

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Answer:

Explanation:

Given that

If you swim at speed in calm water 1.25m/s

Current speed of the water is 1m/s

Let assume you are swimming in positive x-axis, then, Va=1.25 m/s

Then, let assume the river is flowing in the opposite direction, then it will be negative x axis Vr=-1m/s

If you are swimming against the current in a river, then the river is slowing you down.

Therefore, your speed would be

V=Va+Vr

V=1.25•im/s−1.00•im/s = 0.25•im/s

Then, if you moving in the direction of the current the speed will be faster, this is just like when a car is driving down a slope road,

Now if the river and the you are in the same direction, let assume positive x axis

Then, Va=1.25 •i m/s

Vr=1.00 •im/s

Then, V=Va+Vr

v = 1.25•i+ 1•i=2.25 •im/s

The velocities will be 2.25 m/s (downstream) and -0.25 m/s (upstream), taking right direction as positive and left direction as negative, and considering the rivercurrent from left to right.

To solve this question, we must first define a direction convention and assign postive and negative direction with a reference.

Let us assume that the river current is from left to right, so that the right direction positive direction and left direction is negative direction.

We are given that:

The speed of swimmer in calm water, u = 1.25 m/s.

And the speed of river current, v = 1.0 m/s

Now, two cases arise which are as below:

(i) swimming downstream:

that is swimming along the river current, from left to right.

In this case the speed of river current will be added with he speed of the swimmer, so that the final speed in downstream is:

v' = u + v

   = (1.25 + 1.0)m/s

v' = 2.25 m/s is the downstream swimming speed

(ii) swimming upstream:

that is swimming against the river current, from right to left.

in this case the speed of the swimmer is taken negative according to the convention for direction taken above, so the final speed in upstream will be:

v" = -u + v

   = (-1.25 + 1.0) m/s

v" = -0.25 m/s is upstream swimming velocity

The negative sign indicates that the swimmer is going from right to left according to the direction convention taken above.  

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https://brainly.com/question/2235632?referrer=searchResults

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