vector question help!! (1 Viewer)

[poptarts12345]

Two forces, of magnitude p newtons and q newtons, have a resultant of 2√7 N when they act at 90° to each other. When they act at 30° to each other, however, the magnitude of the resultant is 2√13 N. Find the values of p and q.

This question is from the cambridge textbook.

ANS : 2√3 and 4

 

[Trebla]

When they are at right angles you will get



When they are at 30 degrees with each other, note that the resultant vector is the diagonal of a parallelogram which has sides p and q. You can then use the cosine rule to get

 

[jinglebells1464646]

is it possible to do this question without using cosine rule? using just pure vectors?

 

[ISAM77]

Here's my worked solution.

 

[blank.barnhouse928374]

Here's my worked solution.

I can rewrite it neatly if required.

hi, could you please write it out nicely? thanks.

 

[Luukas.2]

is it possible to do this question without using cosine rule? using just pure vectors?

Another approach is to take the forces as and when they are at right angles, so that:

​

And, when at 30 degrees, take one force as and the other as , so that:

​

 

[ISAM77]

hi, could you please write it out nicely? thanks.

Hope it helps.

 

[blank.barnhouse928374]

Hope it helps.

thanks a lot! also nice bg