Question

A plane is flying with an airspeed of 211 miles per hour with heading 248.7°. The wind currents are running at a constant 43.6 miles per hour in the direction 238.6°. Find the ground speed and true course of the plane. (Round your answers to the nearest whole number for the speed and to one decimal place for the angle.)

Answer 1

ok, can you draw a picture to start?

Answer 2

okok

Answer 3

i think

Answer 4

You know what I don't think I'm the person to help you here, @wio @ShadowLegendX , can you help?

Answer 5

if u happen to know someone ... please send them over... by the way.. do i send u that starbucks card?

Answer 6

@Nnesha , can you take a look as well. lol and no, no starbucks card needed

Answer 7

its ok... Ill just wait to ask the professor....

Answer 8

hmm. Guess it's big guns time @phi , can you assist?

Answer 9

u guys are smart

Answer 10

@zepdrix , I haven't done vectors in a long time...

Answer 11

I haven't done a vector problem like this in over ten years probably O.O So, I just cannot remember the format for if the resultant vector type of questions

Answer 12

resultant vector is just the combination of the vector components in the x direction and y direction I think

Answer 13

I believe it is...... \[\vec R = x_i+ y_j\]\[x=l\cos(\theta)\]\[y = m\sin(\theta)\] where l and m are lengths of the respective sides.

Answer 14

The angle the two makes with the horizontal are 68.7 and 58.6
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we'll get the x and y components of both the wind current and the plane
Plane:
\[x_{plane} = 211\cos68.7^o\]
\[x_{plane}=76.646mph\]
\[y_{plane} = 211\sin68.7^o\]
\[y_{plane}=196.5868mph\]
Wind Current:
\[x_{wind~current} = 43.6\cos58.6^o\]
\[x_{wind~current} =22.716mph\]
\[y_{wind~current} = 43.6\sin58.6^o\]
\[y_{wind~current} = 37.2148mph\]
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Since they both go along in the same direction, you'll have the resultant as
\[R = \sqrt{(x_{plane}+x_{wind~current})^2+(y_{plane}+y_{wind~current})^2}\]
\[R \sqrt{(76.646+22.716)^2+(196.5868+37.2148)^2}\]
\[R=254.039mph\]
The angle will be:
\[\tan \theta = \frac{ y_{plane} +y_{wind~current} }{ x_{plane}+x_{wind~current} }\]
\[\tan \theta = \frac{ 196.5868+37.2148 }{ 76.646+22.716 }\]
\[\tan \theta = \frac{ 233.8016 }{ 99.362 }\]
\[\theta = \tan^{-1}\frac{ 233.8016 }{ 99.362 }\\]
\[\theta = 66.975^o\]

Answer 15

Good job! :)

Answer 16

This is for the angles:
248.7-180=68.7
238.6-180=58.6

Answer 17

did you get it so far @itsmecaro ?

Answer 18

wow... sorry

Answer 19

thats amazing.. ok so please guide me here.. how did u come up from subtracting to get the angle between angle and x plane?