Solving Vector Problem: Displacement from Point A

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To solve the displacement problem from point A to point B, the person’s movement can be analyzed using vector components. The Law of Sines and Cosines may be applicable for calculating the resultant vector. To find the components, the vectors should be treated as hypotenuses of right triangles, with trigonometric functions used to determine the opposite and adjacent sides. Specifically, sine and cosine functions will help in calculating the y and x components, respectively. Understanding these concepts will lead to the correct displacement calculation.
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Homework Statement



A person walks from point A to point B as show in the picture below. What is the person's displacement relative to A?
Vector.jpg


Homework Equations



Law of Sines and Cosines?

The Attempt at a Solution



It involves vectors, and I need to divide them up into components.

How do I do that?

Thank you for your help.
 
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The two titles on the right say Fifty meters and 60 degrees.

Thank you.
 
Think of the vectors as the hypotenuses of right triangles. What trig functions would you use to find the opposite and adjacent components? (y and x, respectively)
 
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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