You are on an airplane traveling 30° south of due west at 110.0 m/s with respect to the air. The air is moving with a speed 39.0 m/s with respect to the ground due north.

Question

agent0smith · Answer

Okay... Is there a question?

anonymous · Answer

Oh sorry here it is.
1) What is the speed of the plane with respect to the ground.
2)What is the heading of the plane with respect to the ground? (Let 0° represent due north, 90° represents due easth)

Also if you dont mind i need way how you solve it because I have got an idea how to work with this kind of tasks.

anonymous · Answer

call the velcocity of the plane wrt the air VPA, and the velcocity of the air wrt the ground VAG …
 
velocities are vectors, so they obey the laws of vector addition …
 
you want VPG, which is VPA + VAG …
 
there are two ways to do this …
 
i] draw a vector triangle of the three velocities, with vertices labelled P A and G, and with arrows along each side pointing the correct way, and use the sine and cosine rules
 
ii] use x and y components (separately)

agent0smith · Answer

I think this is what it looks like |dw:1360214693319:dw|

anonymous · Answer

it make sense tnx.
i got write answer by coslaw.
but what about second question?

agent0smith · Answer

I think you just need to find the angle for the heading. Should be able to use the sine rule. |dw:1360217678537:dw|

agent0smith · Answer

$$\frac{ \sin 60 }{x } = \frac{ \sin y }{ 39 }$$

x is what you found for speed, in part a.

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