You bail out of a helicopter and pull the ripcord of your parachute. Now the air resistance proportionality constant is k = 1.53, so your downward velocity satisfies the initial value problem below, where v is measured in ft/s and t in seconds. 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 velocity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity. dv dt = 32-1.53v, v(0) = 0
You bail out of a helicopter and pull the ripcord of your parachute. Now the air resistance proportionality constant is k = 1.53, so your downward velocity satisfies the initial value problem below, where v is measured in ft/s and t in seconds. 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 velocity be? Will a strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity. dv dt = 32-1.53v, v(0) = 0
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How long will it take you to reach 95% of your limiting velocity?
I end up getting 1.56s, however that is the wrong answer. Appreciate the help on how to solve this

Transcribed Image Text:You bail out of a helicopter and pull the ripcord of your parachute. Now the air resistance proportionality constant is k = 1.53, so your downward
velocity satisfies the initial value problem below, where v is measured in ft/s and t in seconds. 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 velocity be? Will a
strategically located haystack do any good? How long will it take you to reach 95% of your limiting velocity.
dv
dt
40
30
20
10
= 32-1.53v, v(0) = 0
1
2
3
4
5
40
30
How long will it take you to reach 95% of your limiting velocity?
About 1.56 second(s)
(Round to the nearest integer as needed.)
20
10
0
0.0
0.2 0.4
0.6
0.8
1.0
What will your limiting velocity be? Will a strategically located haystack do any good? Select the correct choice below and fill in the answer box
to complete your choice.
(Round to the nearest integer as needed.)
A strategically located haystack would help because a limiting velocity of 20 ft/s is quite survivable.
A strategically located haystack would not do any good because a limiting velocity of ft/s is not survivable.
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