Find the direction of the resulatnt vector

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The discussion revolves around calculating the direction of the resultant vector from four given vectors with specified magnitudes and angles. The user has successfully calculated the resultant vector's components but struggles with determining its direction. After an incorrect attempt using the tangent function, another participant suggests that the resultant vector lies in the third quadrant, leading to the correct angle calculation. The user expresses gratitude for the assistance received in resolving the problem. The conversation highlights the challenges of vector addition and the importance of understanding quadrant-specific angle adjustments.
Arshad_Physic
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Hello everyone, here is a question of which Part b is giving me a headache + tension! :) My teacher only gave us 2 days to do so much homework - one day left! :) Its impossible to take help from him...

Homework Statement



Consider four vectors ~F1, ~F2, ~F3, and ~F4,
where their magnitudes are
F1 = 50 N,
F2 = 29 N,
F3 = 27 N, and
F4 = 58 N.

Let
theta1 = 150 degrees,
theta2 = -140 degrees,
theta3 = 24 degrees, and
theta4 = -66 degrees, measured from the positive x axis
with the counter-clockwise angular direction
as positive.

What is the magnitude of the resultant vec-
tor ~F , where ~F = ~F1 + ~F2 + ~F3 + ~F4? Answer
in units of N.

I found the answer to his part:

-17.259 i and -35.645 j , with a magnitude of 39.604

My online homework accepted this answer :)

...BUT...


(part 2 of 2)
What is the direction of this resultant vector
~F?

Note: Give the angle in degrees, use coun-
terclockwise as the positive angular direction,
between the limits of -180 degrees and +180 degrees from
the positive x axis. Answer in units of degrees.


Homework Equations



I tried doing: tan θ = -35.645/-17.259 - θ=64.164 °

The Attempt at a Solution



I tried doing: tan θ = -35.645/-17.259 - θ=64.164 ° - The answer proved out to be wrong...And thus I can now score a maximum of 93% on this question! :(

I have NO IDEA as to how to solve it - I looked in google, but to no avail...All help would be appreciated! :)

Thanks

Arshad
 
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Resultant is in the third quadrant. So theta should be -180 + 64 degrees.
 
You are right! THANKS for the help! :)
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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