What is the angle and displacement of the plane?

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SUMMARY

The discussion focuses on calculating the angle and displacement of an airplane tracked by a radar station. Initially, the plane is detected at a range of 412 meters at an angle of 40° above the horizon. After tracking the plane through an additional 123° in the vertical east-west plane, the final range is determined to be 810 meters. The displacement of the airplane during this observation period is calculated using trigonometric principles and vector analysis.

PREREQUISITES
  • Understanding of trigonometric functions and their applications in physics.
  • Familiarity with vector analysis and displacement calculations.
  • Knowledge of radar tracking principles and coordinate systems.
  • Ability to interpret angles in a two-dimensional plane.
NEXT STEPS
  • Study vector addition and subtraction in two-dimensional motion.
  • Learn about the applications of trigonometry in physics problems.
  • Explore radar technology and its use in tracking moving objects.
  • Review displacement and distance calculations in physics.
USEFUL FOR

Students in physics or engineering courses, educators teaching kinematics, and anyone interested in understanding radar tracking and displacement calculations in real-world scenarios.

mathnerd21

Homework Statement


In the figure below, a radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is d1 = 412 m at 40° above the horizon. The airplane is tracked for another 123° in the vertical east–west plane, the range at final contact being d2 = 810 m. Find the displacement of the airplane during the period of observation.
magnitude ______ meters
direction ______° (counter-clockwise from east)
 
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It would also be helpful if you attached the figure referred to in the problem.
 

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