Overall displacement vector from a walking trip....

[Cayce]

Homework Statement

I start walking. The first leg of my trip I walk 65 meters at 5 degrees south of east. The second leg of my trip I walk 75 meters at 18 degrees north of east. The final leg of my trip I walk 95 meters at 69.5 degrees north of west. Choose the coordinate system so that x is directed towards the east and y is directed towards the north.

Write an expression for the x component of the final displacement in terms of the given quantities.

Write an expression for the y component of the final displacement in terms of the given quantities.

What is the magnitude of my displacement vector (in meters) as measured from the origin?

What is the angle of my displacement vector as measured counterclockwise from the +x axis?

Homework Equations

The Attempt at a Solution

 

[Chestermiller]

Homework Statement

I start walking. The first leg of my trip I walk 65 meters at 5 degrees south of east. The second leg of my trip I walk 75 meters at 18 degrees north of east. The final leg of my trip I walk 95 meters at 69.5 degrees north of west. Choose the coordinate system so that x is directed towards the east and y is directed towards the north.

Write an expression for the x component of the final displacement in terms of the given quantities.

Write an expression for the y component of the final displacement in terms of the given quantities.

What is the magnitude of my displacement vector (in meters) as measured from the origin?

What is the angle of my displacement vector as measured counterclockwise from the +x axis?

Homework Equations

The Attempt at a Solution

Can you draw a sketch of this trip?

 

[Cayce]

Can you draw a sketch of this trip?

I drew what I think is the triangle for this trip but I am confused on how to proceed because the angles only add up to 92.5 and not 180. which i was under the assumption that all triangle angles added up to 180.

 

[Chestermiller]

I drew what I think is the triangle for this trip but I am confused on how to proceed because the angles only add up to 92.5 and not 180. which i was under the assumption that all triangle angles added up to 180.

The question didn't say anything about a triangle. Let's see your sketch.

 

[Cayce]

I can't figure out how to upload the pics for you to see

 

[Chestermiller]

I can't figure out how to upload the pics for you to see

Click on upload beneath the window where you enter text.

 

[Cayce]

I was able to do a few print screens of the homework problem. As you can see I do not need the answer. I have already tried for 2 days and given up so I only received 50% credit for the problem. I want to know how to solve this problem for when it arrives again. I lucked up on the first 2 questions but only because I used the feedback given.

 

[Cayce]

here is my triangle I drew

 

[haruspex]

I drew what I think is the triangle

You seem to be assuming that the trip ends back at the starting point. Given the questions, that is hardly likely.

 

[Cayce]

You seem to be assuming that the trip ends back at the starting point. Given the questions, that is hardly likely.

Ok then here is my problem. I took this course on the basis that it was algebra based physics. We are doing sin, cos, and tan which are trig functions. I have done some tutorials on Khan academy with these functions so that I understand them since I never took trig. The last lecture we spent the entire lecture dealing with triangles so I just assumed this would be a triangle. I don't know where to even start in trying to solve this problem. I am so confused.

 

[Nidum]

I haven't given you the actual diagram for your problem but here are three different examples of the type of diagram that you need to draw .

 

[Ray Vickson]

here is my triangle I drew
View attachment 209747

You should not have a triangle, because your last point does not land back at the starting position.

 

[haruspex]

Ok then here is my problem. I took this course on the basis that it was algebra based physics. We are doing sin, cos, and tan which are trig functions. I have done some tutorials on Khan academy with these functions so that I understand them since I never took trig. The last lecture we spent the entire lecture dealing with triangles so I just assumed this would be a triangle. I don't know where to even start in trying to solve this problem. I am so confused.

You are asked to find the final x displacement. Each of the three legs makes a contribution to that. Can you find those contributions?

 

[Chestermiller]

In the figure, I meant 69.5 degrees rather than 79 degrees.

 

[Ray Vickson]

Ok then here is my problem. I took this course on the basis that it was algebra based physics. We are doing sin, cos, and tan which are trig functions. I have done some tutorials on Khan academy with these functions so that I understand them since I never took trig. The last lecture we spent the entire lecture dealing with triangles so I just assumed this would be a triangle. I don't know where to even start in trying to solve this problem. I am so confused.

Each "leg" of your trip forms a vector (since it has a length and a direction). If you look from the start to the end of the vector AB for the first leg, you go $x$ units in the easterly direction and $y$ units in the northerly direction, so that single portion of the trip can be thought of as a kind of triangle: it has a base $x$ an height $y$, and a 90 degree turn from east to north. In fact, if you walked due east by $x$ units and then due north by $y$ units, you would end up in exactly the same place as in the first leg of the trip. The hypotenuse of your little triangle is, of course, the actual leg of the trip, going off at a certain angle for a certain distance. (Note that if $y< 0$ you go $-|y|$ units north, which is actually $+|y|$ units south. Similarly, a negative easterly step is actually a positive step in the westerly direction.)

Following that you go along another leg of your trip and so you have another vector and hence have another triangle. If you had stopped at a 2-leg trip (AB then BC) you would, indeed get a true triangle ABC whose sides are the first leg AB, the second leg BC and the total vector CA from finish to start.

However, that is NOT what you have: your trip contains a third leg CD, so now the figure ABCDA is a quadrilateral, not a triangle. (If you had made a fourth leg DE your "figure" ABCDEA would now be 5-sided, a kind of pentagon, etc.)

Anyway, for your 3-leg trip, you need to figure out the total displacement you make in the east $(+x)$ direction and the total displacement you make in the north $(+y)$ direction. That will tell you the final position after the third leg of your journey. From that you can figure out how far you are from your starting point, and what would be the angle from the start to the final point.

 

[Cayce]

I have posted a photo of what I tried again with creating triangles and I still can't come up with the answer that they have. What am I doing wrong?

 

[haruspex]

I have posted a photo of what I tried again with creating triangles and I still can't come up with the answer that they have. What am I doing wrong?

You seem to have used 64.75 as the net x displacement, but that is only the x displacement from the first leg.

 

[Nidum]

 

[Ray Vickson]

I have posted a photo of what I tried again with creating triangles and I still can't come up with the answer that they have. What am I doing wrong?

Type out your work, so we can see clearly what you are doing. Your picture does not show the whole solution, so it is impossible to say what you are doing wrong.

 

[Cayce]

View attachment 209788

Thank you so much for this diagram. I kept drawing the wrong triangles which made it impossible to get the right answers. Now that I had the right triangles, I could solve the problem without any issues.