Explore A student walks forward a distance represented by the displacement vecto

Question

Explore
A student walks forward a distance represented by the displacement vector Aof magnitude 7 m, and then walks to obtain an additional displacement Bof length 3.7perpendicular to A. (a) What is the magnitude of the resulting displacement from the origin? (b) What magnitude of total displacement would result if the second displacement were -Binstead of B?

Conceptualize
The length of the arrow representing displacement vector A is proportional to the distance of 7 m thatA represents, and there is a second displacement Bthat is perpendicular to Aof length 3.7 m.

(A) The magnitude of the displacement from the originAnalyze If we sketch a diagram showing the vector addition, with the tail of B appended to the arrowhead representing A, then it becomes clear that the Pythagorean theorem must be used to find the length of R, which is then the resulting magnitude of the displacement. It is equal to

(B) The magnitude when B is changed to -B.Analyze In this case, we can add -B to A, instead of adding B to A. This then becomes

Finalize
The greatest magnitude for A + B results when the two directions are (the same/opposite/perpendicular) ---Select---the sameoppositeperpendicular ?
The smallest magnitude for A + B results when the two directions are (the same/opposite/perpendicular) ---Select---the sameoppositeperpendicular ?

Explanation / Answer

Analyze

A) 7.917

B) 7.917

Finalize

A) same direction

B) opposite direction

Related Questions

Navigate

• Browse (All)
• Browse E
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.