2) Consider a particle of mass m initially at a height h in a fluid. The particle is released and allowed to fall through the fluid. The differential equation that governs its motion is: mä = -mg - yi %3D a) solve for x(t) and v(t). b) Graph (accurately and clearly) the position and velocity as a function of time from t-0 to t=10 for the cases where g-1 and y/m0.2 and 1. Use h-10. c) Derive a general formula for the limiting speed of falling.
2) Consider a particle of mass m initially at a height h in a fluid. The particle is released and allowed to fall through the fluid. The differential equation that governs its motion is: mä = -mg - yi %3D a) solve for x(t) and v(t). b) Graph (accurately and clearly) the position and velocity as a function of time from t-0 to t=10 for the cases where g-1 and y/m0.2 and 1. Use h-10. c) Derive a general formula for the limiting speed of falling.
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Transcribed Image Text:2) Consider a particle of mass m initially at a height h in a fluid, The particle is released and
allowed to fall through the fluid. The differential equation that governs its motion is:
mä = -mg - y*
a) solve for x(t) and v(t).
b) Graph (accurately and clearly) the position and velocity as a function of time from t-0 to t=10
for the cases where g-1 and y/m 0.2 and 1. Use h-10.
c) Derive a general formula for the limiting speed of falling.
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