Help (: adding vectors components.... angles, drawing.

In summary, the problem involves a ship traveling 55 degrees west of north and ending up 65km farther north after 3.0 hours. The goal is to find the ship's velocity. The equation Vground= Vair + Vwind is relevant but it is necessary to determine whether the boat's velocity or ground velocity is being sought. Drawing out the problem and using trigonometric functions will help in solving the problem. The correct answer is 38km/h.
  • #1
britt6

Homework Statement


A ship traveling 55 degrees [W of N] is 65km farther north after 3.0h. What is the ship's velocity.

Homework Equations


sin, cos, tan?

The Attempt at a Solution


I know that Vground= Vair + Vwind, and that Vground = Vboat + Vcurrent, but I'm not sure if that is even relevant to the question... So far I have drawn out :

Do I add these vectors together or subtract? and am I trying to find the boat's velocity or ground velocity. I think boat velocity but what does that make of the 55 degrees W of N... I am so lost please help (:

Screen Shot 2017-07-09 at 7.48.31 PM.png
 
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  • #2
britt6 said:
I have no idea help please!
You need to show some attempt at a solution first before others will try to help you.
Try drawing out the problem at least.
 
  • #3
NFuller said:
You need to show some attempt at a solution first before others will try to help you.
Try drawing out the problem at least.

Ok! I've never used this before lol so I don't know what I'm doing. But thanks, I will do that.
 
  • #4
Your image link appears to be addressing a target that is not publicly accessible. I suggest that you UPLOAD the image file to the PF server so that it's made available t our homework helpers (use the UPLOAD button).
 
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  • #5
gneill said:
Your image link appears to be addressing a target that is not publicly accessible. I suggest that you UPLOAD the image file to the PF server so that it's made available t our homework helpers (use the UPLOAD button).
Thank you!
 
  • #6
On your image you've labelled the distances x and y. y is the distance that the boat traveled in the northward direction, and presumably x is distance it traveled in the westward direction. Can you determine the total distance it traveled along its trajectory? (hint: what's the length of the hypotenuse of that triangle?)
 
  • #7
gneill said:
On your image you've labelled the distances x and y. y is the distance that the boat traveled in the northward direction, and presumably x is distance it traveled in the westward direction. Can you determine the total distance it traveled along its trajectory? (hint: what's the length of the hypotenuse of that triangle?)

Now I am not sure... Do I use v=d/t. The answer in the book says its 38km/h but that doesn't seem to match up with my numbers.
 

Attachments

  • Screen Shot 2017-07-09 at 8.33.58 PM.png
    Screen Shot 2017-07-09 at 8.33.58 PM.png
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  • #8
Your evaluation of c doesn't look right. Please show your calculation in detail. What is a? What is b?
 
  • #9
Oops I see where I made a mistake.. instead of putting a as 65 squared, I put 95 squared. Just a calculation error! Thanks for your help, I've figured out the question now (:
 

1. How do I add vector components?

To add vector components, you need to break each vector into its x and y components. Then, simply add the x components together and the y components together to get the resulting vector.

2. What is the process for finding the angle between two vectors?

To find the angle between two vectors, you can use the dot product formula: A · B = |A||B|cosθ. First, find the magnitudes of the two vectors. Then, take the dot product of the two vectors. Finally, use inverse cosine to solve for θ.

3. How do I draw vectors on a graph?

To draw vectors on a graph, you will need to plot the starting point of the vector, and then use the magnitude and direction to determine the endpoint. You can use a protractor to measure the angle and a ruler to measure the magnitude.

4. What is the relationship between vector components and angles?

The x and y components of a vector can be used to calculate the magnitude and direction of the vector using trigonometric functions. The angle of the vector can be found using the inverse tangent function: θ = tan⁻¹(y/x).

5. Can you add vectors with different angles?

Yes, you can add vectors with different angles. However, you will need to use trigonometric functions to find the resulting vector's magnitude and direction. You can also use the parallelogram method or the head-to-tail method to visually add vectors with different angles.

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