If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a massm dropped from a given height is determined from dv m = mg - kv, k> 0. dt Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s. (a) Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.) v(5) = ft/s (b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6]. 50아 50 50F 5아 40 40 40 40 30 30 30 30 20 20 20 20 10 10 10 10 1 3 4 5 6 1 2 3 6 1 2 3 4 5 6 1 2 3 4 5 6 (c) Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.) v(5) = ft/s
If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a massm dropped from a given height is determined from dv m = mg - kv, k> 0. dt Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s. (a) Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.) v(5) = ft/s (b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6]. 50아 50 50F 5아 40 40 40 40 30 30 30 30 20 20 20 20 10 10 10 10 1 3 4 5 6 1 2 3 6 1 2 3 4 5 6 1 2 3 4 5 6 (c) Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.) v(5) = ft/s
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from
mov = mg - kv², k> 0.
dt
Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s?.
(a) Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.)
v(5) =
ft/s
(b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6].
V
V
V
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50
50
50
40
40
40
40
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30
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10F
10
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10
t
t
6
t
t
1
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2
4
(c) Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.)
v(5) =
ft/s](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6f51a47d-2c3a-4935-8f76-d9a574028b9a%2F7f034032-962f-4ca9-9ea5-9e818be5c57f%2Fsyx7jit_processed.png&w=3840&q=75)
Transcribed Image Text:If air resistance is proportional to the square of the instantaneous velocity, then the velocity v of a mass m dropped from a given height is determined from
mov = mg - kv², k> 0.
dt
Let v(0) = 0, k = 0.125, m = 8 slugs, and g = 32 ft/s?.
(a) Use the RK4 method with h = 1 to approximate the velocity v(5). (Round your answer to three decimal places.)
v(5) =
ft/s
(b) Use a numerical solver to graph the solution of the IVP on the interval [0, 6].
V
V
V
50
50
50
50
40
40
40
40
30
30
30
30
20
20
20
20
10F
10
10
10
t
t
6
t
t
1
3
4
3
4
4
2
4
(c) Use separation of variables to solve the IVP and then find the actual value v(5). (Round your answer to four decimal places.)
v(5) =
ft/s
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