2. Slow moving landslides can move ('creep') at rates ranging from millimetres to several metres per year. Although they rarely claim lives, they can cause major damage to property and infrastructure. Depending on seasonal rainfall, they can accelerate or decelerate. Figure 2: A slow-moving landslide in Ponzano, Italy. Image credit: https://www.geoengineer.org/ne ws/italian-village-is-being-torn-apart-by-slow-moving-landslide In risk mitigation and early warning systems for landslide hazards, an important property of landslides that is monitored using radar technology is the so-called inverse velocity, y(t) = v(t) where V(t) is the landslide's velocity. Consider a slow moving landslide like that in the village of Ponzano, Italy (Figure 2). Suppose the inverse velocity y(t) is governed by the equation 4y -y² +45 dy dt where t is the time in years since the start of monitoring. (a) Write this ODE in form dy dt arctant et/2 (t≥ 0, y > 0) + P(t) y = Q(t) yn for some n, and use a suitable substition u = ya to reduce this differential equation to a linear first order ODE. Hint: look in the lecture slides for a suitable substitution to use for Bernoulli's equation. (b) Solve the ODE to find y(t) in terms of t, given the initial condition y(0) = 2. (c) Is the landslide moving faster or slower at t = 1 than at the start of monitoring? You might need to use a calculator or computer to help with this.
2. Slow moving landslides can move ('creep') at rates ranging from millimetres to several metres per year. Although they rarely claim lives, they can cause major damage to property and infrastructure. Depending on seasonal rainfall, they can accelerate or decelerate. Figure 2: A slow-moving landslide in Ponzano, Italy. Image credit: https://www.geoengineer.org/ne ws/italian-village-is-being-torn-apart-by-slow-moving-landslide In risk mitigation and early warning systems for landslide hazards, an important property of landslides that is monitored using radar technology is the so-called inverse velocity, y(t) = v(t) where V(t) is the landslide's velocity. Consider a slow moving landslide like that in the village of Ponzano, Italy (Figure 2). Suppose the inverse velocity y(t) is governed by the equation 4y -y² +45 dy dt where t is the time in years since the start of monitoring. (a) Write this ODE in form dy dt arctant et/2 (t≥ 0, y > 0) + P(t) y = Q(t) yn for some n, and use a suitable substition u = ya to reduce this differential equation to a linear first order ODE. Hint: look in the lecture slides for a suitable substitution to use for Bernoulli's equation. (b) Solve the ODE to find y(t) in terms of t, given the initial condition y(0) = 2. (c) Is the landslide moving faster or slower at t = 1 than at the start of monitoring? You might need to use a calculator or computer to help with this.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
Related questions
Question
100%
Transcribed Image Text:2. Slow moving landslides can move ('creep') at rates ranging from millimetres to several metres
per year. Although they rarely claim lives, they can cause major damage to property and
infrastructure. Depending on seasonal rainfall, they can accelerate or decelerate.
Figure 2: A slow-moving landslide in Ponzano, Italy. Image credit: https://www.geoengineer.org/ne
ws/italian-village-is-being-torn-apart-by-slow-moving-landslide
In risk mitigation and early warning systems for landslide hazards, an important property of
landslides that is monitored using radar technology is the so-called inverse velocity, y(t) = v(t)
where V(t) is the landslide's velocity.
Consider a slow moving landslide like that in the village of Ponzano, Italy (Figure 2). Suppose
the inverse velocity y(t) is governed by the equation
4y -y² +45
dy
dt
where t is the time in years since the start of monitoring.
(a) Write this ODE in form
dy
dt
arctant
et/2
(t > 0, y > 0)
+ P(t) y = Q(t) yn
for some n, and use a suitable substition u = ya to reduce this differential equation to a
linear first order ODE.
Hint: look in the lecture slides for a suitable substitution to use for Bernoulli's equation.
(b) Solve the ODE to find y(t) in terms of t, given the initial condition y(0) = 2.
(c) Is the landslide moving faster or slower at t = 1 than at the start of monitoring?
You might need to use a calculator or computer to help with this.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Functions and Change: A Modeling Approach to Coll…
Algebra
ISBN:
9781337111348
Author:
Bruce Crauder, Benny Evans, Alan Noell
Publisher:
Cengage Learning
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill