Vector Calculation: Find Angle & Magnitude Resultant Vector

[AlchemistK]

Homework Statement

Two forces of 30N and 40N act on a particle such that the resultant vector makes an angle of 30 degrees with the first vector. What is the angle between the given vectors and magnitude of the resultant vector?


I know of vector addition, but i can't find out the angle between the vectors in this one, if i know the angle, i can figure out the rest.

Thank you.

 

[gneill]

Perhaps a diagram will help?

 

[AlchemistK]

Yes i figured out the diagram myself but i still can't find the value of $$\theta$$ .

 

[gneill]

What equations have you written that relate the various triangle sides and the angles?

 

[AlchemistK]

i used tan 30^o = Bsin$$\theta$$ / A + B cos$$\theta$$
to find $$\theta$$ but after a bit complex solving i reached to cos$$\theta$$ = 5/8
which i don't think is correct.
If i get to know the angle i can use R=$$\sqrt{}A^2 + B^2 -2AB cos\theta$$

 

[gneill]

Perhaps you need to demonstrate your "complex solving" so that we can see what's going wrong. It seems like you're starting along a good path. So, given A = 30 and B = 40,

tan(30°) = 1/√3 = Bsinθ / (A + Bcosθ)

continue...

 

[AlchemistK]

I realize it contains some unnecessary steps, but i hope that doesn't make it wrong.

 

[gneill]

That looks good. Only you've solved for cos(θ), not θ itself. Take the arccos of it to find θ.

 

[AlchemistK]

oh yeah, i actually meant cos $$\theta$$ , on solving, $$\theta$$ = 51^o (approx.) which i think isn't right.

 

[AlchemistK]

OH! wait! it is 51! Now i feel like a fool...

Sorry for wasting you time.

 

[gneill]

OH! wait! it is 51! Now i feel like a fool...

Sorry for wasting you time.

No worries. Glad to help.