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MMMU-Pro / test_Mechanical_Engineering_420 / A test projectile is fired horizontally into a viscous liquid with a velocity…

Problem

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question

A test projectile is fired horizontally into a viscous liquid with a velocity v0. The retarding force is proportional to the square of the velocity, so that the acceleration becomes a = -kv^2. Derive expressions for the distance D traveled in the liquid and the corresponding time t required to reduce the velocity to v0 /2. Neglect any vertical motion.<image 1>

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Diagrams

options

t=2/kv0, D=(ln4)/k
t=3/kv0, D=(ln2)/k
t=1/kv0,D=(ln2)/k
t=2/kv0,D=(ln2)/k
t=1/kv0, D=(ln5)/k
t=3/kv0, D=(ln3)/k
t=2/kv0, D=(ln3)/k
t=1/kv0, D=(ln4)/k
t=1/kv0,D=(ln3)/k

subject

Mechanical_Engineering

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Source and history

upstream_id / Original problem ID: test_Mechanical_Engineering_420
task_id: f62b111e-aa8b-5996-b4e7-11e13ebeeac7
task_key: standard~20~2810~20options~29--test--test~5fMechanical~5fEngineering~5f420
task_revision_id: 3
config / split: standard (10 options) / test

Official source

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