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If an airplane is flying at 300 km /h to the east and is facing a headwind of 18.0 km/h what is the airplane's final velocity

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The problem states that the airplane is flying at 300 km/h. This is absolute, thus 300 km/h East is your final answer. That assumes this problem is a trick problem that is worded correctly. 

Assuming this is not a trick problem, and is worded incorrectly, to find the final velocity you just sum them. A headwind is wind going against the airplane, so 18 km/h headwind makes the airplane go 282 km/h. If it were a tailwind, you would add.

Answer:

[tex]v_{net} = 282 km/h[/tex]

Explanation:

Airplane is moving with speed of 300 km/h

so this is the absolute speed with which airplane by which it can fly in still air

so here if air is also moving with some speed then the net speed of the plane in ground frame would be different

So here we can say

[tex]v_{net} = \vec v_p + \vec v_{air}[/tex]

now when head wind is blowing then in that case the speed of plane is opposite to the motion of the plane

so here we have

[tex]v_{net} = 300 - 18[/tex]

[tex]v_{net} = 282 km/h[/tex]

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