Why Is My Calculation for the X Component of the Vector Sum Incorrect?

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The discussion revolves around calculating the x and y components of the vector sum of two vectors, each with a magnitude of 13.0 m and angles of 30° and 100°. The user believes the y component is correctly calculated as 16.3 but struggles with the x components, arriving at 9.0 after summing 11.26 and -2.26. Another participant questions the accuracy of the y component, suggesting that the magnitudes might actually be 11.0 m instead. The confusion highlights the importance of correctly applying trigonometric functions to determine vector components.
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The two vectors a and b have equal magnitudes of 13.0 m and their angles are θ1 = 30° and θ2 = 100°.
Find the components of their vector sum, r.


I know this is a very simple problem, but I can't get it! And it is frustrating me to no end.

I know the y component of the sum is 16.3. (I don't remember how I got this, but it's right.)
However, when I try to find the x components of each vector, I get 11.26 for a, and -2.26 for b. When these are added, you get 9.0. And the computer(our HW is graded online) is telling me that this is the wrong answer.

What am I doing wrong?!
 
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STEF2098 said:
The two vectors a and b have equal magnitudes of 13.0 m and their angles are θ1 = 30° and θ2 = 100°.
Find the components of their vector sum, r.
…
I know the y component of the sum is 16.3. (I don't remember how I got this, but it's right.)
However, when I try to find the x components of each vector, I get 11.26 for a, and -2.26 for b. When these are added, you get 9.0. And the computer(our HW is graded online) is telling me that this is the wrong answer.

What am I doing wrong?!

Hi STEF2098! :smile:

hmm … I make it 9.0 also, but I don't get 16.3 :confused:

are you sure it's not |a| = |b| = 11.0 m?
 
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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