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MMLU-Pro / 9232 / Top gun" pilots have long worried about taking a turn too tightly. As a pilot's…

Problem

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question

"Top gun" pilots have long worried about taking a turn too tightly. As a pilot's body undergoes centripetal acceleration, with the head toward the center of curvature, the blood pressure in the brain decreases, leading to loss of brain function. There are several warning signs. When the centripetal acceleration is 2g2 g or 3g3 g, the pilot feels heavy. At about 4g4 g, the pilot's vision switches to black and white and narrows to "tunnel vision." If that acceleration is sustained or increased, vision ceases and, soon after, the pilot is unconscious - a condition known as gg-LOC for " gg-induced loss of consciousness." What is the magnitude of the acceleration, in gg units, of a pilot whose aircraft enters a horizontal circular turn with a velocity of v→i=(400i^+500j^)m/s\vec{v}_i=(400 \hat{\mathrm{i}}+500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s} and $24.0 \mathrm{~s}$ later leaves the turn with a velocity of v→f=(−400i^−500j^)m/s\vec{v}_f=(-400 \hat{\mathrm{i}}-500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s} ?
Plain-text mathematical notation (without MathML)
"Top gun" pilots have long worried about taking a turn too tightly. As a pilot's body undergoes centripetal acceleration, with the head toward the center of curvature, the blood pressure in the brain decreases, leading to loss of brain function.
There are several warning signs. When the centripetal acceleration is 2g or 3g, the pilot feels heavy. At about 4g, the pilot's vision switches to black and white and narrows to "tunnel vision." If that acceleration is sustained or increased, vision ceases and, soon after, the pilot is unconscious - a condition known as g-LOC for " g-induced loss of consciousness."

What is the magnitude of the acceleration, in g units, of a pilot whose aircraft enters a horizontal circular turn with a velocity of (v)→_(i)=(400(i)^+500(j)^)m/s and $24.0 \mathrm{~s}$ later leaves the turn with a velocity of (v)→_(f)=(−400(i)^−500(j)^)m/s ?
Original LaTeX notation
"Top gun" pilots have long worried about taking a turn too tightly. As a pilot's body undergoes centripetal acceleration, with the head toward the center of curvature, the blood pressure in the brain decreases, leading to loss of brain function.
There are several warning signs. When the centripetal acceleration is $2 g$ or $3 g$, the pilot feels heavy. At about $4 g$, the pilot's vision switches to black and white and narrows to "tunnel vision." If that acceleration is sustained or increased, vision ceases and, soon after, the pilot is unconscious - a condition known as $g$-LOC for " $g$-induced loss of consciousness."

What is the magnitude of the acceleration, in $g$ units, of a pilot whose aircraft enters a horizontal circular turn with a velocity of $\vec{v}_i=(400 \hat{\mathrm{i}}+500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$ and $24.0 \mathrm{~s}$ later leaves the turn with a velocity of $\vec{v}_f=(-400 \hat{\mathrm{i}}-500 \hat{\mathrm{j}}) \mathrm{m} / \mathrm{s}$ ?

category

physics

options

  1. 95.67 $\mathrm{m} / \mathrm{s}^2$
  2. 62.48 $\mathrm{m} / \mathrm{s}^2$
  3. 83.81 $\mathrm{m} / \mathrm{s}^2$
  4. 72.14 $\mathrm{m} / \mathrm{s}^2$
  5. 110.87 $\mathrm{m} / \mathrm{s}^2$
  6. 75.19 $\mathrm{m} / \mathrm{s}^2$
  7. 100.56 $\mathrm{m} / \mathrm{s}^2$
  8. 55.92 $\mathrm{m} / \mathrm{s}^2$
  9. 90.43 $\mathrm{m} / \mathrm{s}^2$
  10. 68.25 $\mathrm{m} / \mathrm{s}^2$

src

scibench-fund

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Source and history

upstream_id / Original problem ID
9232
task_id
f0b053b6-57b0-50fc-ae63-8732907d5379
task_key
default--test--9232
task_revision_id
1
config / split
default / test

Official source

initial import