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

[burton95]

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

v_m,g = v_w,g + v_w,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?

 

[haruspex]

The water is actually traveling in a negative x direction so how do I account for that?

By using minus signs
Pls post your working.

 

[burton95]

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

 

[HallsofIvy]

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 [itex]v_{mm}$are <b>vectors</b>, not numbers?$[/itex]

 

[burton95]

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

 

[burton95]

I found it. Just going through the motions of showing the work helps tremendously. Thanks folks