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MMLU-Pro / 9373 / In an orienteering class, you have the goal of moving as far (straight-line…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) $\vec{a}, 2.0 \mathrm{~km}$ due east (directly toward the east); (b) $\vec{b}, 2.0 \mathrm{~km} 30^{\circ}$ north of east (at an angle of 30∘30^{\circ} toward the north from due east); (c) $\vec{c}, 1.0 \mathrm{~km}$ due west. Alternatively, you may substitute either −b→-\vec{b} for b→\vec{b} or −c→-\vec{c} for c→\vec{c}. What is the greatest distance you can be from base camp at the end of the third displacement? (We are not concerned about the direction.)
Plain-text mathematical notation (without MathML)
In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) $\vec{a}, 2.0 \mathrm{~km}$ due east (directly toward the east); (b) $\vec{b}, 2.0 \mathrm{~km} 30^{\circ}$ north of east (at an angle of 30^(∘) toward the north from due east); (c) $\vec{c}, 1.0 \mathrm{~km}$ due west. Alternatively, you may substitute either −(b)→ for (b)→ or −(c)→ for (c)→. What is the greatest distance you can be from base camp at the end of the third displacement? (We are not concerned about the direction.)
Original LaTeX notation
In an orienteering class, you have the goal of moving as far (straight-line distance) from base camp as possible by making three straight-line moves. You may use the following displacements in any order: (a) $\vec{a}, 2.0 \mathrm{~km}$ due east (directly toward the east); (b) $\vec{b}, 2.0 \mathrm{~km} 30^{\circ}$ north of east (at an angle of $30^{\circ}$ toward the north from due east); (c) $\vec{c}, 1.0 \mathrm{~km}$ due west. Alternatively, you may substitute either $-\vec{b}$ for $\vec{b}$ or $-\vec{c}$ for $\vec{c}$. What is the greatest distance you can be from base camp at the end of the third displacement? (We are not concerned about the direction.)

category

physics

options

  1. 4.2 m
  2. 4.6 km
  3. 3.8 km
  4. 2.9 km
  5. 5.2 km
  6. 3.5 m
  7. 4.8 m
  8. 5.0 km
  9. 5.6 m
  10. 3.2 km

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9373
task_id
20807c95-6a37-552c-80ef-b2250875245c
task_key
default--test--9373
task_revision_id
1
config / split
default / test

Official source

initial import