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

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In summary, the problem involves finding the speed of a person swimming relative to the ground while the river current is flowing at a speed of 1.5 m/s in a northwest direction. The equation used is vm,g = vw,g + vw,m, where vw,g is the speed of the water relative to the ground and vw,m is the speed of the person relative to the water. By converting the direction of the current to a vector, solving for its components, and plugging in the given values, the final answer is determined to be 1.67 m/s.
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burton95
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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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  • #2
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.
 
  • #3
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
 
  • #4
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 [itex]v_{wg}[/itex] and [itex]v_{mm}[itex] are vectors, not numbers?
 
  • #5
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
 
  • #6
I found it. Just going through the motions of showing the work helps tremendously. Thanks folks
 

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

1. What is a vector quantity?

A vector quantity is a type of physical quantity that has both magnitude and direction. Some examples of vector quantities include velocity, acceleration, and force.

2. How do you calculate the speed in m/s relative to ground using vectors?

To calculate the speed in m/s relative to ground, you would first need to find the magnitude of the velocity vector. This can be done by using the Pythagorean theorem where the x-component and y-component of the velocity vector are the two sides of a right triangle. Once you have the magnitude, you can divide it by the time taken to travel that distance to get the speed in m/s.

3. What information is needed to solve vector problems?

To solve vector problems, you will need to know the magnitude and direction of the vectors involved. You will also need to consider the coordinate system being used and any relevant equations or formulas.

4. How do you find the direction of the velocity vector?

The direction of the velocity vector can be found by using trigonometric functions such as tangent or sine, depending on the given information. It is also important to note the quadrant in which the vector lies in order to correctly determine the direction.

5. How can vector problems be applied in real life situations?

Vector problems have many real-life applications, such as in navigation, engineering, and physics. For example, vector addition can be used to determine the resultant force of multiple forces acting on an object, which is important in engineering and construction. Vectors are also used in GPS systems to determine location and direction of travel, making them essential in navigation.

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