help with vector/magnitude question

[adrian]

hi can anyone help me understand this question:

Two forces, P and Q, act on a mass. The resultant of P and Q is a force with magnitude 10N and acts on a bearing of 055. If force P has a magnitude of 12N and acts due north find the magnitude and bearing of force Q.

I'm trying to answer the question using vectors and construct a triangle but getting muddled as to how I should construct the triangle and which side is which. I've been given the answer as 10.3N, 127.4 degrees but still can't seem to work it out...
thanks in advance

 

[daon2]

I will use standard degrees, so 055->35 degrees.

You have P+Q = <10cos(35), 10sin(35)>, and P=<0,12>. Solving for Q gives: Q=<10cos(35), 10sin(35)-12>

Can you find the magnitude and angle of this vector?

 

[Deleted member 4993]

hi can anyone help me understand this question:

Two forces, P and Q, act on a mass. The resultant of P and Q is a force with magnitude 10N and acts on a bearing of 055. If force P has a magnitude of 12N and acts due north find the magnitude and bearing of force Q.

I'm trying to answer the question using vectors and construct a triangle but getting muddled as to how I should construct the triangle and which side is which. I've been given the answer as 10.3N, 127.4 degrees but still can't seem to work it out...
thanks in advance

Do not quite understand - what does that statement mean? Is that 055°? If it is - why didn't you define it?

 

[HallsofIvy]

"On a bearing of 55 degrees" means 55 degrees from North. Of course "north" could be anything in this problem but the fact that the other "acts due north" means that the angle between the two vectors is 55 degrees. Adrian, if you draw one vector on the other, so that they "add" and the resultant is the third side of a triangle, you have two sides of length 10 and 12 with angle between them 55 degrees. You can use the cosine law to find the length of the third side (the magnitude of Q) and then use the sine law to find the other angles in the triangle and, from that, the bearing of Q.

 

[mmm4444bot]

"On a bearing of 55 degrees" means 55 degrees from North.

It makes no difference in this exercise, but I can never remember whether the terminal ray rotates from the initial ray (i.e., due north) clockwise or counterclockwise with a bearing measurement such as this.

In other words, I would require no storm to end up on Gilligan's Island.

How do you remember?

 

[HallsofIvy]

My mind is stockpile of useless trivia! Also I used to (not so much anymore) do quite a bit of navigating with a compass.