Calculate the velocity of the canoe relative to the water

[waltssillyhat]

Homework Statement

Tessa is canoeing across a river with a current of 2.5 m/s to the west.

a) Her resultant velocity (relative to the ground) is 3.6 m/s north. Calculate the velocity of the canoe relative to the water.

b) The current increases to 3.1 m/s west, but Tessa continues with the same velocity relative to the water. What is her resultant velocity relative to the ground?

Relevant Equations

Relative motion calculation

I calculated part a of the question and I found the correct solution, which was 4.4m/s N35degE, but I don't understand how to find Tessa's velocity relative to the ground in part b using her velocity relative to the water which I found in part a.

 

[PeroK]

The same concepts are required for both parts of the problem. Part b) should be another vector addition.

Note that there is a quick way by decomposing the new current into the old current plus the increase. But, perhaps, you should do it the standard way first.

 

[Chestermiller]

Let's see your work for part (a).

 

[waltssillyhat]

sorry the photo is flipped to the side for some reason

 

[Chestermiller]

In part (a), what are the components of her velocity relative to the water (taking east as positive and west as negative)?

In part (b), what is the east-west component of her velocity relative to the water and relative to the ground?

 

[Lnewqban]

Welcome, @waltssillyhat !

 

[waltssillyhat]

Welcome, @waltssillyhat !


View attachment 358068

why did you draw that red curved line?

 

[Lnewqban]

why did you draw that red curved line?

Because the problem tells us that Tessa is rowing at a constant speed respect to the water for any circumstances.
That circle represents the many directions that a velocity vector (V_TR) of that magnitude could take.

That direction would be perfectly vertical and pointing North if the velocity of the current respect to ground was zero (V_R=0).

That direction would be perfectly horizontal and pointing East if the velocity of the current respect to ground was equal or greater than your calculated V_TR.

 

[PeroK]

Because the problem tells us that Tessa is rowing at a constant speed respect to the water for any circumstances.

It's a constant velocity. I don't understand the circle.