Answered: What rate values for snowfall and/or…

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

What rate values for snowfall and/or snow removal would allow h(t) to become zero? Can you explain your reasoning and process? I'd think increasing the rate of snow removal to above the rate of snowfall (say 61%) would allow all snow to be cleared at some point but I am not sure. Thanks

Expert Solution

Step 1: General information

To make the height of the snow, h(t), become zero, we need to change the balance between the rate of snowfall and the rate of snow removal. In the original differential equation :

$fraction numerator d h over denominator d t end fraction equals 3 over 5 minus 9 over 20 h$

Here in this equation the right-hand side represents the rate of change of the snow height. To $h left parenthesis t right parenthesis$ reach zero, we want to find the conditions under which this rate becomes positive. In other words, we want the rate of snowfall $3 over 5$ to exceed the rate of snow removal $9 over 20 h$ .