Calculate Plane Velocity Relative to Ground in Different Directions

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SUMMARY

The discussion focuses on calculating the velocity of a small plane with an airspeed of 200 km/h in various directions while considering a wind speed of 50.0 km/h from the east. The pilot's directional adjustments include east, west, north, and north-east orientations. The key takeaway is the necessity of using the head-to-tail method for vector addition, particularly for non-right angle vectors, as demonstrated in the fourth scenario where the correct velocity relative to the ground is 240 km/h at 41° north of east.

PREREQUISITES
  • Understanding of basic vector addition
  • Familiarity with the head-to-tail method for vector resolution
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Basic physics concepts related to velocity and motion
NEXT STEPS
  • Study vector addition techniques, focusing on the head-to-tail method
  • Learn about resolving vectors into components using trigonometric functions
  • Explore the concept of relative velocity in physics
  • Review examples of vector problems involving wind and aircraft navigation
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and vector analysis, as well as anyone interested in aviation dynamics and navigation principles.

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Homework Statement



The airspeed of a small plane is 200 km/h. The wind speed is 50.0 km/h [E]. Determine the velocity of the plane
relative to the ground if the pilot keeps the plane pointing in each of the following directions.
a) East (250 km/h [E] )
b) West (150 km/h [W] )
c) North (206 km/h [N14.0°E])
d) North 40° East (2.4e2 km/h [E41°N] )

Homework Equations


Sin Theta = opp/hyp where Theta = 40 deg, Hyp=200.

The Attempt at a Solution



The first three are basic. For the fourth obviously, a simple resolution of vectors won't do. If I do, I get 128, while the answer is 240. What am I doing wrong?

Sorry to sound so stupid, I am a novice at physics. :confused:
 
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The Pythagorean method is only useful for adding vectors that form a right angle. What other methods of vector addition have you covered?
 
OK, I got it. Thanks. I have to use the head to tail method.
 

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