Starting from point A, Ajit walks 14 metres west. He turns right and walks 14…
2013
Starting from point A, Ajit walks 14 metres west. He turns right and walks 14 metres, then turns left and walks 10 metres. He turns left again, walks 14 metres, and reaches point E. What is the shortest distance between A and E?
Answer: D. 24 — ConceptRepresent each move as a displacement on two perpendicular axes. A right or left turn is determined from the traveller’s current facing direction. The…
- A.
38
- B.
42
- C.
52
- D.
24
Attempted by 10 students.
Show answer & explanation
Correct answer: D
Concept
Represent each move as a displacement on two perpendicular axes. A right or left turn is determined from the traveller’s current facing direction. The shortest distance from start to finish is found from the net horizontal and vertical displacements using the Pythagorean distance formula.
Application
Take A = (0, 0), east as the positive x-direction, and north as the positive y-direction.
After walking 14 metres west, Ajit is at (-14, 0). Facing west, a right turn points north; after 14 metres he is at (-14, 14).
Facing north, a left turn points west; after another 10 metres he is at (-24, 14).
Facing west, a left turn points south; after 14 metres he reaches E = (-24, 0).
Thus the net horizontal displacement is 24 metres west and the net vertical displacement is 0 metres. The distance is √((-24)2 + 02) = 24 metres.
Cross-check
The 14-metre northward and 14-metre southward movements cancel. The two westward movements add to 14 + 10 = 24 metres, so E lies exactly 24 metres west of A.