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You bail out of the helicopter ripcord of your parachute. Now k = 1.6 your downward velocity satisfies the initial value problem and pull the so dv 32-1.6υ, υ(0 ) -0. In order to investigate your chances of survival, construct a slope field for this differential equation and sketch the appropriate solution curve. What will your limiting veloc- ity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity?

You bail out of the helicopter ripcord of your parachute. Now k = 1.6 your downward velocity satisfies the initial value problem and pull the so dv 32-1.6υ, υ(0 ) -0. In order to investigate your chances of survival, construct a slope field for this differential equation and sketch the appropriate solution curve. What will your limiting veloc- ity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity?

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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You bail out of the helicopter ripcord of your parachute. Now k = 1.6 your downward velocity satisfies the initial value problem and pull the so dv 32-1.6υ, υ(0 ) -0. In order to investigate your chances of survival, construct a slope field for this differential equation and sketch the appropriate solution curve. What will your limiting veloc- ity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity?
Transcribed Image Text:You bail out of the helicopter ripcord of your parachute. Now k = 1.6 your downward velocity satisfies the initial value problem and pull the so dv 32-1.6υ, υ(0 ) -0. In order to investigate your chances of survival, construct a slope field for this differential equation and sketch the appropriate solution curve. What will your limiting veloc- ity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity?
Expert Solution
Step 1

Given that, 

                 dvdt=32-1.6v,    v(0)=0.

Step 2

Now, 

                    dvdt=32-1.6v⇒   dvdt+1.6v=32.

Which is a linear equation in v.

By comparing the above equation with the following

equation, we have

               dvdt+P(t)v=Q(t),

Here,

              P(t)=1.6, & Q(t)=32.

For Integrating factor (I.F.):

     I.F.=e∫P(t)dt       =e∫1.6dt       =e1.6t.

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