Vector Addition and Flight Planning

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The discussion focuses on calculating the correct heading for an airplane flight affected by wind. The navigator needs to determine the heading that compensates for an 80 km/h wind from the west while maintaining a desired airspeed of 300 km/h at a direction of 30 degrees east of north. Two methods are suggested for solving the problem: using the law of sines and cosines or converting vectors to rectangular components. A diagram is referenced to illustrate the relationship between airspeed, wind speed, and the resultant ground speed. The conversation highlights the importance of accurately visualizing vector addition for successful flight planning.
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Homework Statement



The navigator of an airplane plans a flight from one airport to another 1200 km away, in a direction 30 degrees east of north. The weather office informs him of a prevailing wind from the west, of 80 km/h. The pilot wants to maintain an air speed of 300 km/h.

a) What heading should the navigator give to the pilot?

b) How long will the flight take?

c) How much time did the wind save?


The Attempt at a Solution



I drew the diagram out, but i didnt know how to solve it.
 
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There are two approaches. You can use law of sines and law of cosines to solve the triangle, or you can convert all your vectors to rectangular x and y components and work out the x and y parts separately.
 
Untitled.png


i was wondering if this diagram was correct?
 
No, it should be like this:
plane2.jpg

The red airspeed plus the windspeed adds up to a vector going at the desired angle 30 degrees E of N (groundspeed).
 
kk thank you, no wonder i kept getting the wrong answer
 
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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