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Consider a radar station C at a busy airport in a city. Currently, the landing runway is busy so the two planes A and B are orbiting in circular paths with a path center at O and their speeds are constant as shown in the figure below. Both planes are at a uniform height h = 1.5 mile from the ground station. The radius of path for plane A is b = 10 mile and the radius of path for plane B is c = 20 mile. The speed of plane Ais u₁ = 200 mi/hr and the speed of plane B is up = 225 mi/hr. Perform the following calculations: a) At the given instant shown ẞ = 30°, what are the position, velocity and acceleration vectors of planes A and B as observed from the station C? Express results in cylindrical coordinates (ur,A,e,a,uz,A and ûr,B,ûe,B,ûz,B for plane A and B respectively). b) At the given instant, what is the relative velocity and acceleration of plane B as observed by the pilot in plane A and express the results in cartesian coordinates. c) What is the shortest time required from current position shown so that the relative distance between planes A and B is minimum? d) Provide the new position, velocity and acceleration of planes A and B in their new location found in part (c) and express the results in cylindrical coordinates as observed from the radar station C(ur,A,ue,A,ûz,A and ûr,B,ûe,B,ûz,B for plane A and B respectively).

Consider a radar station C at a busy airport in a city. Currently, the landing runway is busy so the two planes A and B are orbiting in circular paths with a path center at O and their speeds are constant as shown in the figure below. Both planes are at a uniform height h = 1.5 mile from the ground station. The radius of path for plane A is b = 10 mile and the radius of path for plane B is c = 20 mile. The speed of plane Ais u₁ = 200 mi/hr and the speed of plane B is up = 225 mi/hr. Perform the following calculations: a) At the given instant shown ẞ = 30°, what are the position, velocity and acceleration vectors of planes A and B as observed from the station C? Express results in cylindrical coordinates (ur,A,e,a,uz,A and ûr,B,ûe,B,ûz,B for plane A and B respectively). b) At the given instant, what is the relative velocity and acceleration of plane B as observed by the pilot in plane A and express the results in cartesian coordinates. c) What is the shortest time required from current position shown so that the relative distance between planes A and B is minimum? d) Provide the new position, velocity and acceleration of planes A and B in their new location found in part (c) and express the results in cylindrical coordinates as observed from the radar station C(ur,A,ue,A,ûz,A and ûr,B,ûe,B,ûz,B for plane A and B respectively).

University Physics Volume 1
University Physics Volume 1
18th Edition
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:William Moebs, Samuel J. Ling, Jeff Sanny
Chapter2: Vectors
Section: Chapter Questions
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Solve part A

Consider a radar station C at a busy airport in a city. Currently, the landing runway is busy so the two planes A and B are orbiting in circular paths with a path center at O and their speeds are constant as shown in the figure below. Both planes are at a uniform height h = 1.5 mile from the ground station. The radius of path for plane A is b = 10 mile and the radius of path for plane B is c = 20 mile. The speed of plane Ais u₁ = 200 mi/hr and the speed of plane B is UB = 225 mi/hr. Perform the following calculations: a) At the given instant shown ẞ = 30°, what are the position, velocity and acceleration vectors of planes A and B as observed from the station C? Express results in cylindrical coordinates (ûr,A,ûe,A,ûz,A and ûr,B,Û‚B, Ûz‚ß for plane A and B respectively). b) At the given instant, what is the relative velocity and acceleration of plane B as observed by the pilot in plane A and express the results in cartesian coordinates. c) What is the shortest time required from current position shown so that the relative distance between planes A and B is minimum? d) Provide the new position, velocity and acceleration of planes A and B in their new location found in part (c) and express the results in cylindrical coordinates as observed from the radar station C(ûr,A,e,a,ûz,A and ûr,B,Û0,B, Ûz,B for plane A and B respectively). HINT: Use convenient Coordinate System(s), Coordinate System Transformations and Relative Analysis to make your calculations easier. B Ив C 180° A UA R y
Transcribed Image Text:Consider a radar station C at a busy airport in a city. Currently, the landing runway is busy so the two planes A and B are orbiting in circular paths with a path center at O and their speeds are constant as shown in the figure below. Both planes are at a uniform height h = 1.5 mile from the ground station. The radius of path for plane A is b = 10 mile and the radius of path for plane B is c = 20 mile. The speed of plane Ais u₁ = 200 mi/hr and the speed of plane B is UB = 225 mi/hr. Perform the following calculations: a) At the given instant shown ẞ = 30°, what are the position, velocity and acceleration vectors of planes A and B as observed from the station C? Express results in cylindrical coordinates (ûr,A,ûe,A,ûz,A and ûr,B,Û‚B, Ûz‚ß for plane A and B respectively). b) At the given instant, what is the relative velocity and acceleration of plane B as observed by the pilot in plane A and express the results in cartesian coordinates. c) What is the shortest time required from current position shown so that the relative distance between planes A and B is minimum? d) Provide the new position, velocity and acceleration of planes A and B in their new location found in part (c) and express the results in cylindrical coordinates as observed from the radar station C(ûr,A,e,a,ûz,A and ûr,B,Û0,B, Ûz,B for plane A and B respectively). HINT: Use convenient Coordinate System(s), Coordinate System Transformations and Relative Analysis to make your calculations easier. B Ив C 180° A UA R y
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