An airplane travels 500 miles northeast and then, on the return trip, travels 500 miles southwest. Which of the following is true?

Question

An airplane travels 500 miles northeast and then, on the return trip, travels 500 miles southwest. Which of the following is true??  
A. The displacement of the plane is 1,000 miles, and the distance traveled is 0 miles.  
B. The displacement of the plane is 1,000 miles, and the distance traveled is 1,000 miles.  
C. The displacement of the plane is 0 miles, and the distance traveled is 0 miles.  
D. The displacement of the plane is 0 miles, and the distance traveled is 1,000 miles.

Accepted Answer

Correct Answer: (D)The displacement of the plane is 0 miles, and the distance traveled is 1,000 miles.. 
Rationale: The airplane's displacement equals zero miles while its total distance traveled equals 1,000 miles after flying 500 miles northeast and returning 500 miles southwest.Displacement measures net position change as a vector quantity, canceling to zero when motion returns to the origin, whereas distance accumulates all path segments as a scalar quantity regardless of direction reversals.A) The displacement of the plane is 1,000 miles, and the distance traveled is 0 miles.Displacement cannot equal 1,000 miles when the airplane returns to its origin, displacement would be zero in that case. Simultaneously, distance cannot be zero when the aircraft physically traversed 1,000 miles of airspace. This option incorrectly swaps and misapplies both definitions, violating basic kinematic principles.B) The displacement of the plane is 1,000 miles, and the distance traveled is 1,000 miles.While the distance calculation is correct (500 + 500 = 1,000 miles), displacement cannot be 1,000 miles because displacement depends solely on the net position change. Since northeast and southwest are opposite directions, the return journey cancels the initial displacement vector, resulting in zero net displacement rather than additive magnitude.C) The displacement of the plane is 0 miles, and the distance traveled is 0 miles.Though displacement correctly equals zero (returning to start), distance cannot be zero after physically traveling 1,000 miles through space. Distance accumulates all path segments regardless of direction changes, making zero distance physically impossible after any actual motion occurs.D) The displacement of the plane is 0 miles, and the distance traveled is 1,000 miles.The airplane begins and ends at the same location after traveling equal distances in opposite directions (northeast then southwest), yielding zero displacement, the vector difference between identical initial and final positions. Meanwhile, distance sums all path segments: 500 miles out plus 500 miles back equals 1,000 miles total path length traversed.ConclusionDisplacement measures net position change as a vector quantity, becoming zero when motion returns to the origin, while distance measures total path length as a scalar quantity that accumulates regardless of direction. This distinction proves essential in navigation, sports analytics, and physics problem-solving where path geometry affects outcomes differently than net position change.

An airplane travels 500 miles northeast and then, on the return trip, travels 500 miles southwest. Which of the following is true?

The airplane's displacement equals zero miles while its total distance traveled equals 1,000 miles after flying 500 miles northeast and returning 500 miles southwest.

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