Hard Vectors Q (1 Viewer)

[mreditor16]

I have successfully drawn my diagram. But I am a bit lost with this Q, any help is appreciated!!

 

[photastic]

Vector AB = (-18sin18, 18cos18)
Vector BC = (25sin36, 25cos36)
Vector CD = (20sin72, -25cos72)
Vector DF = (-15sin25, -15cos25)

Vector AF = Vector AB + Vector BC + Vector DC + Vector DF

Then find the distance and angle.

FINAL EDIT

 

[mreditor16]

Vector AB = (-18sin18, 18cos18)
Vector BC = (25sin36, 25cos36)
Vector DC = (20sin76, -25cos76)
Vector DF = (-15sin25, -15cos25)

Vector AF = Vector AB + Vector BC + Vector DC + Vector DF

Then find the distance and angle.

oh we can do that? can anyone confirm?

 

[InteGrand]

I have successfully drawn my diagram. But I am a bit lost with this Q, any help is appreciated!!

This Q seems pretty tedious IMO.

We seek the vector .

From given data, we have the following:









(assuming I haven't made any careless errors).

Now,



.

Now you can compute the angle and magnitude of , as desired.


EDIT: Actually, , so

 

[InteGrand]

oh we can do that? can anyone confirm?

Yes, except the vector coordinates should be flipped to what was written, since and (assuming the first coordinate was the x one).

Edit: maybe the ones written by photastic are right, written with different angles (haven't checked them thoroughly).

 

[photastic]

Yes, except the vector coordinates should be flipped to what was written, since and (assuming the first coordinate was the x one).

Edit: maybe the ones written by photastic are right, written with different angles (haven't checked them thoroughly).

We both get the 28km I believe, I just follow what my tutor tells me

 

[InteGrand]

We both get the 28km I believe, I just follow what my tutor tells me

Well my one gets about 29.8777 km and an angle of 66.2384 degrees East of North, what did I do wrong?

 

[InteGrand]

Vector AF = Vector AB + Vector BC + Vector DC + Vector DF

Then find the distance and angle.

Wait, shouldn't the second last vector be a , not a ...

 

[photastic]

Well my one gets about 29.8777 km and an angle of 66.2384 degrees East of North, what did I do wrong?

I believe your vectors are incorrect. I don't understand how you got those angles though.

Wait, shouldn't the second last vector be a , not a ...

why?

 

[mreditor16]

I got the 28 as well.

 

[InteGrand]

Vector DC = (20sin76, -25cos76)

Where did the 76 come from?

 

[mreditor16]

Wait, shouldn't the second last vector be a , not a ...

yeh Integrand is right, but the expression photastic provided for DC is actually the expression for CD hahaahahah

 

[mreditor16]

Where did the 76 come from?

it was a typo, he meant 72 instead of 76.

doing the method (as a whole) suggested by photastic works

 

[photastic]

Where did the 76 come from?

Should be 72

 

[InteGrand]

I believe your vectors are incorrect. I don't understand how you got those angles though.

For , we are told B is 18 degrees north-west of A, so if you drew A at the origin, B would be on a line 108 degrees, assuming you start at 0 on the positive x-axis and go counter-clockwise.

Similarly for the others.

 

[InteGrand]

why?

Because the order matters. You go from A to B, then B to C, then C to D (hence ), then D to F, to get from A to F.

 

[InteGrand]

OK, I found my error. I should have used the complement of the angle I gave for BC. That gets the 28 km and 51.15 deg East of North.

 

[mreditor16]

I get 57 degrees :/

 

[InteGrand]

I get 57 degrees :/

Angle from positive side of x-axis is:




Then the bearing angle turns out to be , since the vector is in the first quadrant.

 

[mreditor16]

Can anyone identify the flaw in my vectors?

AB = (-18 sin (18 degrees), + 18 cos (18 degrees))

BC = (25 sin (36 degrees), + 25 cos (36 degrees))

CD = (+20 cos (18 degrees), - 20 sin (18 degrees))

DF = (-15 sin (25 degrees), - 15 cos (25 degrees))