Physics: Relative And Circular Motion
Physics

Tutor: None Selected  Time limit: 1 Day 
You are on an airplane traveling 30° south of due west at 160 m/s with respect to the air. The air is moving with a speed 41 m/s with respect to the ground due north.
1.How far west will the plane travel in 1 hour?
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The air is moving with a speed 30 m/s with respect to the ground due north
Airplane is moving with a speed 160 m/s with respect to air due west.
We have to first find the speed of Airplane with respect to the ground.
Since the wind is having a speed of 30 m/s , it will move the air plane toward North as for as the earth is concerned .
Hence we add the speed with the plane’s speed and find the resultant ot these two speeds.
Since they are perpendicular to each other, the resultant is
√ (160 ^2 + 30^2) = 162.79 m/s and the direction is given by tan θ = western velocity / northern velocity so that θ is the angle measured from North to west.
tan θ = 30 / 160 and θ = 10.6° west of north .
Therefore the speed of airplane is 162.79 m/s at angle 10.6° west of north viewed from the ground.
Distance moved in one hour = 160*60*60 =576, 000 m. Therefore in one hour, the airplane would have traveled 576, 000 meters.
I hope this helps!
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I sincerely apologize for that error. The answer would change to 165.2 m/s (instead of 162.79 previously calculated).
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