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You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 7.75 x 103 m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P, = 7.75 × 10°j m. At t = 30.0 s the position vector leading from you to the airplane is Pa0 = (7.82 x 10³i + 7.75 x 10³j) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 65.0 s. magnitude direction o above the horizontal P P

You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 7.75 x 103 m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P, = 7.75 × 10°j m. At t = 30.0 s the position vector leading from you to the airplane is Pa0 = (7.82 x 10³i + 7.75 x 10³j) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 65.0 s. magnitude direction o above the horizontal P P

Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
5th Edition
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Raymond A. Serway, John W. Jewett
Chapter1: Introduction And Vectors
Section: Chapter Questions
Problem 7CQ
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You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 7.75 x 10° m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P, = 7.75 x 10°j m. At t = 30.0 s the position vector leading from you to the airplane is P20 = (7.82 x 10°î + 7.75 x 10°j) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 65.0 s. P30 magnitude direction o above the horizontal Po P30
Transcribed Image Text:You are standing on the ground at the origin of a coordinate system. An airplane flies over you with constant velocity parallel to the x axis and at a constant height of 7.75 x 10° m. At t = 0, the airplane is directly above you so that the vector leading from you to it is P, = 7.75 x 10°j m. At t = 30.0 s the position vector leading from you to the airplane is P20 = (7.82 x 10°î + 7.75 x 10°j) m as suggested in the figure below. Determine the magnitude and orientation of the airplane's position vector at t = 65.0 s. P30 magnitude direction o above the horizontal Po P30
(a) At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 10.5 yards, back (in the -x-direction), then 15.0 yards parallel to the y-axis (in the -y-direction). He then throws the football straight downfield 60.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? yards (b) What if? The receiver that catches the football travels 63.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run? yards
Transcribed Image Text:(a) At a football game, imagine the line of scrimmage is the y-axis. A player, starting at the y-axis, runs 10.5 yards, back (in the -x-direction), then 15.0 yards parallel to the y-axis (in the -y-direction). He then throws the football straight downfield 60.0 yards in a direction perpendicular to the y-axis (in the +x-direction). What is the magnitude of the displacement (in yards) of the ball? yards (b) What if? The receiver that catches the football travels 63.0 additional yards at an angle of 45.0° counterclockwise from the +x-axis away from the quarterback's position and scores a touchdown. What is the magnitude of the football's total displacement (in yards) from where the quarterback took the ball to the end of the receiver's run? yards
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