What is the Angle Between Two Vectors with Equal Magnitudes and a Given Sum?

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To find the angle between two vectors A and B with equal magnitudes of 23.0 and a resultant vector of 12.1 j, one can start by drawing the resultant vector and the two vectors that create it. Using the law of cosines, the relationship R^2 = P^2 + Q^2 + 2PQcos(theta) can be applied, where R is the magnitude of the resultant. Given the magnitudes of A and B, this formula allows for the calculation of the angle between the vectors. The discussion emphasizes the importance of visualizing the vectors and employing trigonometric principles to solve the problem. Understanding these concepts is crucial for accurately determining the angle between the two vectors.
Melchior25
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Hey everyone,

So I'm completely stumped on this question and I have no clue on how to even start. Any help would be greatly appreciated.

Vectors A and B have equal magnitudes of 23.0. If the sum of A and B is the vector 12.1 j, determine the angle between A and B.

Thanks in advance.
 
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Draw the resultant vector of magnitude 12.1N first, then draw the two vectors A and B that would give the resultant direction in the direction that you drew the 12.1N force in. Complete the parallelogram. Then use some trigonometry.
 
In this case, to save a lot of time, I would suggest the OP just use the formula for the magnitude of the resultant R of two forces P and Q, given by:

R^2 = P^2 + Q^2 + 2PQcos(theta).

The magnitude of R is given.
 
Yeah I could agree, just use the law of cosines.
 
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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