Answered: a) Solve your differential equation for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

**coffee filter has mass 0.01908 kg

total stack mass m = 12 × 0.01908 = 0.22896 kg

AveVelInitial = y3 − y1/t3-t1 = 1.10446 m/s

t = 0 at the second observation of our collected data

distance fallen here is 0 m

initial velocity of 1.10446 m/s.

v(t) = (g−1/2m*ρACvo2)t+c

Where variables are

g is acceleration due to gravity

ρ is density of airC is drag coefficient

A is the cross sectional area of the object

vo is the initial velocit

m is mass of stacked coffee filters **

a) Solve your differential equation for v(t)
b) If you choose to solve the equation in v(t), the velocity, then you can integrate the velocity function you obtained, v(t), above to get position function

Time (s)
Distance (m)
Time (s)
Distance (m)
0.00
0.0000
0.22
0.3619
0.02
0.0228
0.24
0.4050
0.04
0.0478
0.26
0.4500
0.06
0.0730
0.28
0.4931
0.08
0.1054
0.30
0.5440
0.10
0.1369
0.32
0.5927
0.12
0.1710
0.34
0.6429
0.14
0.2063
0.36
0.6937
0.16
0.2426
0.38
0.7458
0.18
0.2810
0.40
0.7991
0.20
0.3197
0.42
0.8556
Table 1. Data on the time and position of a stack of coffee filters as it falls to the
ground. We measure the distance falling positively downward and say y(t) is the
distance fallen in meters at time t in seconds, i.e. t is time in seconds from release
and y(t). is distance in meters fallen from release.

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