Solve Vector Prob: Find Speed in m/s Relative to Ground

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The problem involves calculating the swimmer's speed relative to the ground while swimming east at 2 m/s against a northwest river current of 1.5 m/s. The swimmer's velocity vector is represented as 2i, while the river's current is decomposed into its components, resulting in a vector of -1.062i + 1.368267j. By summing these vectors, the resultant velocity relative to the ground is found to be approximately 1.67 m/s. The discussion emphasizes the importance of understanding vector components and using proper calculations to arrive at the correct answer. Engaging with the problem and showing work is highlighted as beneficial for understanding.
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Homework Statement



The current in a river is flowing northwest with a speed of 1.5 m/s. You are swimming due east with a speed of 2 m/s relative to the water. What is your speed (in m/s) relative to the ground?

Homework Equations


vm,g = vw,g + vw,m

The Attempt at a Solution



I have tried all sorts of playing around getting answers such as .5, 2.5, 3. I set x to the east as positive and y north positive. The water is actually traveling in a negative x direction so how do I account for that?
 
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burton95 said:
The water is actually traveling in a negative x direction so how do I account for that?
By using minus signs :smile:
Pls post your working.
 
I don't know if I'd call it work but i just plugged in the values that were given in the the problem into the equation stated. The different answers come from different combos of these numbers and then i checked them against an online quiz. Something tells me i have to turn these into a parametric equation but I am at a loss
 
Please show your work! You say "i just plugged in the values that were given in the the problem into the equation stated." I suspect that the problem is that you do not understand the equation. Do you understand that v_{wg} and v_{mm}are <b>vectors</b>, not numbers?
 
I will show my work. I apologize...I was posting from my phone on the bus ride home last night and this morning.

My next thought it to try and deconstruct -1.5 m/s NW into i and j. Using θ=45 in quad 2 for NW I tried to solve -1sin (x/-1.5) = 45 and came up with -1.062. Then set 1.5 = ((1.062)2 + (x)2)1/2 and solved x = 1.368267.

Vw,g = -1.062i + 1.368267j
Vm,w = 2i

Vm,g = Vw,g + Vm,w = -1.062i + 1.368267j + 2i

= .938i + 1.368267j

(.9382+1.3682672)1/2 = 1.67 m/s

I'm sure I'm all over the place
 
I found it. Just going through the motions of showing the work helps tremendously. Thanks folks
 

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