Airplanes and vertex

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Airplanes and vertex

Mathematics
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velocity of jet is 775 mi/h in NE direction : |dw:1433303568557:dw|
can you split it as horizontal and vertical components ?
em nah i'm not sure.
you mean like make it into triangles?
Yes solve these two sides in the right triangle |dw:1433304188744:dw|
the side along j is 548.007 ...right?
no, sorry. the side from the j line to the plane
548 is right
oh haha good!
|dw:1433304779704:dw|
so for part \(b\), the velocity of jet in component form is \[\large 548i + 548j\]
ok!
can we do the same for the wind and get 27.5? or does that not work?
you need to work horizontal and vertical components in this triangle |dw:1433306300948:dw|
horozontal = 55*sin(30) = ? vertical = 55*cos(30) = ?
27.5 47.63
(horizontal first, vertical second)
is the direction of the jet (the last box) = 58.64?
(sorry, tht's a completely different part. we can come back to that.)
good so for part \(a\) do we have \[\large 27.5i + 47.63j\] ?
Yup
For part \(c\), simply add the answers from part \(a\) and \(b\)
hey may be use 548.0077i + 548.0077j for part a because they are asking to round to two decimal places
part \(c\) : true velocity of plane = velocity of plane + velocity of wind = \(\large (548.007i+548.007j) + (27.5i+47.63j)\) = ?
575.51i +595.62j
you should be getting 575.51i +595.6\(\color{red}{4}\)j check once
hm ok. Maybe i rounded the numbers wrong. I tried to use the original numbers.
ok part \(d\) should be simple take the magnitude of true velocity vector from part \(c\)
speed = \(\|575.51i+595.64j\| = \sqrt{575.51^2+595.64^2}=?\)
828.25
knw how to work last part ?
uh well I think so but i've been getting lots wrong lately lol
for last part, just need to find the angle of true velocity vector from part \(c\)
equation for that would be?
For any vector \(x+iy\), angle with positive x axis is given by \(\tan^{-1}(y/x)\)
so we'd do tan^(-1) 595.64/575.51
yes use ur calculator
45.98
oh but rounded to nearest interger so 46?
yes but thats the angle from positive x axis : |dw:1433308877835:dw|
the question is asking you for the angle from positive "y" axis
|dw:1433308980730:dw|
44
Perfect!
haha yay! :)
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Did i put them in wrong? o.o because the answers based off of those are correct.
how many chances do u have ?
5!
5 or 5!=120
try putting exact form
oh gosh no lol just 5.
part \(a\) : \[\large 27.5i+27.5\sqrt{~3~} j\]
part \(b\) : \[\large 387.5\sqrt{2}i+387.5\sqrt{2}j\]
Yeah the example one they did looks sort of like that. just divided b by the sq2
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good, give it a try you have 3 more chances right
so should I do it exactly like them and try to put little arrows over stuff?
do u knw how to put arrows ?
maybe forget about arrows for now and try entering the exact values wid radicals if it doesn't work, then you may try with arrows
because part c worked even when you didn't put arrows
not dividing it by sq2 either?
enter these and let me know if they work http://gyazo.com/81f10a84809d5f9dc852b18b923080a3
Yep that did it :)
Awesome!
Many thanks ^-^
np

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