Why is the following situation impossible? A shopper pushing...

Why is the following situation impossible? A shopper pushing a cart through a market follows directions to the canned goods and moves through a displacement 8.00 ì m down one aisle. He then makes a $90.0^{\circ}$ turn and moves $3.00 \mathrm{~m}$ along the $y$ axis. He then makes another $90.0^{\circ}$ turn and moves $4.00 \mathrm{~m}$ along the $x$ axis. Every shopper who follows these directions correctly ends up $5.00 \mathrm{~m}$ from the starting point.

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Key Concepts

Consistency Checks in Problem Statements

This involves verifying that the numerical values given in a problem align with the mathematical operations applied, such as vector addition and the Pythagorean theorem. Inconsistent or contradictory values indicate that the prescribed movements cannot yield the specified overall displacement.

Pythagorean Theorem

The Pythagorean theorem is used to calculate the magnitude of the resultant displacement vector when the movements are along perpendicular directions. By squaring the individual components of the displacement vector and taking the square root of their sum, one can determine if the net displacement is consistent with the given magnitudes.

Displacement

Displacement refers to the overall change in position from the starting point to the end point, represented as a vector. It differs from the total distance traveled along the path, since it only considers the direct, straight-line distance and direction.

Vector Addition

This concept involves combining multiple displacement vectors to produce a single resultant vector. In problems involving movements in different directions, each movement can be expressed as a vector, and the overall displacement is the sum of these vectors obtained by adding their corresponding components.

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