What is the displacement after traveling on two different compass headings?

In summary: The angle should be between the positive x direction and the resultant vector, which is the vector sum of A and B. You can use trigonometry to find this angle, or you can use inverse trigonometric functions. Inverse trigonometric functions are designed to help you find an angle when you know two sides of a right triangle. Do you know of a right triangle you can make with the information you have?In summary, the problem involves a person traveling on a compass heading of 15.0 degrees west of south for 23.4km, and then turning 20.5 degrees east of south and traveling an additional 32.0km. The question asks for the person's displacement, which can
  • #1
Scooter I
12
0

Homework Statement



I set out on a compass heading of 15.0 degrees west of south for 23.4km.

I turn 20.5 degrees east of south and travel another 32.0km.

What is my displacement?



Homework Equations



I'm not sure if there are any. But these should help.

Ax = A cos θ
Ay = A sin θ
Bx = B cos θ
By = B sin θ

The Attempt at a Solution



Alright, I'm not sure at all of this but:

Ax = -23.4km cos 75 = -6.05
Ay = -23.4 sin 75 = -22.6

That's all I've come up with. Can someone tell me if I'm doing this right, and guide me through the process of finding a solution?

Thanks in advance.
 
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  • #2
Scooter I said:

Homework Statement



I set out on a compass heading of 15.0 degrees west of south for 23.4km.

I turn 20.5 degrees east of south and travel another 32.0km.

What is my displacement?



Homework Equations



I'm not sure if there are any. But these should help.

Ax = A cos θ
Ay = A sin θ
Bx = B cos θ
By = B sin θ

The Attempt at a Solution



Alright, I'm not sure at all of this but:

Ax = -23.4km cos 75 = -6.05
Ay = -23.4 sin 75 = -22.6

That's all I've come up with. Can someone tell me if I'm doing this right, and guide me through the process of finding a solution?

Thanks in advance.

I believe you have the trig functions backwards. DRAW A DIAGRAM and that shall be confirmed one way or the other. [Actually I don't know why you are using 75 degrees]
When you sketch the diagram, your 15 degree angle might not be exact - unless you use a protractor, but it should be a lot less than 45 degrees. Otherwise you will lose the guidance of your picture, and will have wasted your time drawing it in the first place.
 
  • #3
Scooter I said:
Alright, I'm not sure at all of this but:

Ax = -23.4km cos 75 = -6.05
Ay = -23.4 sin 75 = -22.6
Hello Scooter I. Welcome to PF !

These are correct !

Do likewise for Bx & By .

Then add like components together.
 
  • #4
Can anyone else verify that I'm doing it correctly...? I really don't think so.
 
  • #5
Ax and Ay seem correct to me.

Do the same with Bx and By, Bx should be positive and By should be negative as you have defined North and East to be the positive directions.

Add the components so you have a total x displacement and total y displacement, then use pythagoras theroem to find total distance.

Edit: Also you're are asked to find displacement which is a vector quantity i assume you also need to find the angle as well as the distance. Oce you have found the total x displacement and total y displacement, you can work this you by drawing a triangle and using trigonometry.
 
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  • #6
well in fact you just need the angle in between your vectors.

|A+B|= SQRT( A^2 + B^2 + 2 cosθ AB)
On the right side are the magnitudes and not vectors

θ= 15.0 deg + 20.5deg .
Because they are west and east the total angle you can find is the Thita1 of the vector 1 to South and Thita2 of the vector 2 to south.

Now you put numbers and it's finished
 
  • #7
Scooter I said:
Can anyone else verify that I'm doing it correctly...? I really don't think so.

Because you changed to 75 degrees, rather than using to the 15 degree angle given, you original expressions were correct.

I hope you have drawn a diagram - if you have you would be more confident of any answers you calculate - by relating it to that diagram.
 
Last edited:
  • #8
Would B be: Bx = 32.0km
By = 32.0km sin 75 = 30.9km

And then the angle would be 17 degrees? But I don't know what direction.
 
  • #9
Scooter I said:
Would B be: Bx = 32.0km
By = 32.0km sin 75 = 30.9km

And then the angle would be 17 degrees? But I don't know what direction.

Have you drawn a diagram yet? That will show you the direction!
 

FAQ: What is the displacement after traveling on two different compass headings?

1. How do you add vectors?

To add vectors, you must first determine the direction and magnitude of each vector. Then, you can use the head-to-tail method or the parallelogram method to find the resultant vector. In the head-to-tail method, you place the tail of one vector at the head of the other and draw a line from the tail of the first vector to the head of the second vector. The resultant vector is the line from the tail of the first vector to the head of the second vector. In the parallelogram method, you draw the two vectors as sides of a parallelogram and the resultant vector is the diagonal of the parallelogram.

2. What is the resultant vector?

The resultant vector is the vector that represents the combined effect of two or more vectors. It is found by adding the individual vectors using the head-to-tail or parallelogram method.

3. Can you add vectors with different magnitudes?

Yes, you can add vectors with different magnitudes. The resultant vector will have a direction and magnitude that is determined by the individual vectors being added.

4. How do you determine the direction of the resultant vector?

The direction of the resultant vector is determined by the direction of the individual vectors being added. If the vectors are in the same direction, the resultant vector will also be in that direction. If the vectors are in opposite directions, the resultant vector will be in the direction of the larger vector.

5. Why is vector addition important in science?

Vector addition is important in science because it allows us to represent and analyze complex physical systems. Many physical quantities, such as force, velocity, and displacement, can be represented as vectors. By adding these vectors, we can determine the overall effect of different forces or motions on an object. This is crucial in fields such as physics, engineering, and astronomy.

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