Oversimplified Vector Calculus Problem

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SUMMARY

The discussion centers on the validity of a vector calculus problem involving wind velocity and airplane speed. The wind velocity, v1, is 40 mph from east to west, while the airplane's airspeed, v2, is 100 mph due north. A participant argues that the speed of the airplane relative to the ground cannot simply be calculated as the vector sum of v1 and v2 due to the influence of drag forces and the assumption of constant velocity. The conversation emphasizes the importance of adhering to the problem's given conditions regarding constant speeds.

PREREQUISITES
  • Understanding of vector addition in physics
  • Familiarity with the drag equation in aerodynamics
  • Knowledge of constant velocity concepts
  • Basic principles of relative motion
NEXT STEPS
  • Study the effects of drag on aircraft performance
  • Learn about vector decomposition in physics
  • Research the implications of constant velocity in real-world scenarios
  • Explore advanced topics in aerodynamics and flight dynamics
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Students in physics or engineering, educators teaching vector calculus, and aviation professionals interested in the dynamics of flight and wind effects on aircraft performance.

XYZeagle
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I'm not asking for a solution to this problem. I'm just wondering about its validity.

Homework Statement



The wind velocity v1 is 40mph from east to west while an airplane travels with air speed v2 of 100mph due north. The speed of the airplane relative to the ground is the vector sum v1 + v2.


I completely disagree that the speed of the plane relative to the ground is the vector sum v1 + v2. The speed of the object would be changed by a force predicted by the drag equation. It's velocity also is also not constant with time.
 
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Presumably the airspeed takes drag into effect. As far as velocity being constant in time, here you are arguing with information given in the problem. The wind and plane speeds are given as constant in this problem. Choosing to not accept the given hypotheses is really not an option.
 
Mark44 said:
Presumably the airspeed takes drag into effect. As far as velocity being constant in time, here you are arguing with information given in the problem. The wind and plane speeds are given as constant in this problem. Choosing to not accept the given hypotheses is really not an option.

You know the speed of the plane before it encounters wind and the speed of the wind. The drag force caused by the wind will accelerate the plane, thus the changing velocity of the plane over time.
 
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