A small airplane takes of at an airspeed of 180km/h, at an angle of inclination of 14 degrees toward the east. A 15 km/h wind is blowing from the southwest. Determine the resultant ground velocity.

Question

shamim · Answer

i think i will b able to solve it

anonymous · Answer

It's something to do with the unit vectors, but after I get them, I'm at a loss because I don't know what's next to do with them. The one with the initial air speed's unit vectors are: x=180scos14, and y=180sin14

anonymous · Answer

But after that, I'm lost

shamim · Answer

so u wanna know the resultant ground velocity

shamim · Answer

i think wind velocity will b $$15i-15j$$

shamim · Answer

and the result of ur question will b $$180 \cos 14+15 \cos 45$$

shamim · Answer

m i right

shamim · Answer

do u wanna c details

anonymous · Answer

Details please. Sorry for the late reply

shamim · Answer

ok

shamim · Answer

the ground component of the plane speed of 180 km/h is 
180cos14

shamim · Answer

and this ground component is along east

shamim · Answer

next the component along east of wind speed  (15) is  15 cos 45

shamim · Answer

then i just add those

anonymous · Answer

And it's 45 degrees because of the fact that it's coming STRAIGHT from the SW right?

shamim · Answer

ya i think so

anonymous · Answer

how would you get the angle?

shamim · Answer

i guessed

anonymous · Answer

Alright. I'll try to get it in some way :P. Thanks for the help

shamim · Answer

thanks for medal

shamim · Answer

anyway if u wanna know just the resultant velocity of ur plane then the result will b different

anonymous · Answer

How would you get the resultant plane velocity?

shamim · Answer

i wanna introduce unit vector here

anonymous · Answer

i and j being x and y respectively

shamim · Answer

ya  i,j,k  will b along X,Y  and Z  axis

shamim · Answer

unit vector

anonymous · Answer

And then, how do you get an absolute answer from those?

shamim · Answer

ok

shamim · Answer

i was wrong

shamim · Answer

actually the plane velocity will b   180 cos 14 i+180 sin 14 k

anonymous · Answer

Alright, then you just add those and get the answer?

shamim · Answer

ya

shamim · Answer

n we can get absolute number too

shamim · Answer

now wind velocity will b    15 cos 45 i+15 sin 45j

shamim · Answer

so the resultant velocity of ur plane will b    180 cos14i+15cos45i+15sin45j+180sin14k

shamim · Answer

absolute is $$r=\sqrt{x ^{2}+y ^{2}+z ^{2}}$$