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

[Scooter I]

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.

 

[PeterO]

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.

 

[SammyS]

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 B_x & B_y .

Then add like components together.

 

[Scooter I]

Can anyone else verify that I'm doing it correctly...? I really don't think so.

 

[The1337gamer]

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.

 

[Morgoth]

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

 

[PeterO]

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.

 

[Scooter I]

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.

 

[PeterO]

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!