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MMLU-Pro / 8857 / A ball is thrown eastward into the air from the origin (in the direction of the…

Problem

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

question

A ball is thrown eastward into the air from the origin (in the direction of the positive xx-axis). The initial velocity is 50i+80k50 \mathrm{i}+80 \mathrm{k}, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4ft/s24 \mathrm{ft} / \mathrm{s}^2, so the acceleration vector is a=−4j−32k\mathbf{a}=-4 \mathbf{j}-32 \mathbf{k}. What speed does the ball land?
Plain-text mathematical notation (without MathML)
 A ball is thrown eastward into the air from the origin (in the direction of the positive x-axis). The initial velocity is 50i+80k, with speed measured in feet per second. The spin of the ball results in a southward acceleration of 4ft/s², so the acceleration vector is a=−4j−32k. What speed does the ball land?
Original LaTeX notation
 A ball is thrown eastward into the air from the origin (in the direction of the positive $x$-axis). The initial velocity is $50 \mathrm{i}+80 \mathrm{k}$, with speed measured in feet per second. The spin of the ball results in a southward acceleration of $4 \mathrm{ft} / \mathrm{s}^2$, so the acceleration vector is $\mathbf{a}=-4 \mathbf{j}-32 \mathbf{k}$. What speed does the ball land?

category

math

options

  1. $16\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  2. $18\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  3. $14\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  4. $9\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  5. $8\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  6. $20\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  7. $12\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  8. $5\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  9. $10\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$
  10. $15\sqrt{93}$ $\mathrm{ft}/\mathrm{s}$

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8857
task_id
353459dc-125e-5306-b0d4-ffd8b166c3c1
task_key
default--test--8857
task_revision_id
1
config / split
default / test

Official source

initial import