Can I get an easy explanation 4The motion of an object falling from rest under gravity, subject to a drag forceproportional to the square of the speed, may be modelled by the initial value problem(IVP):(b)(c)Here v is the speed of the object, t is time, g is gravitational acceleration (assumedconstant) and is a constant.(a)Without solving the IVP, briefly describe how you expect v to vary with t.(d)dvdt(e)=g- &v², v(0)=0.Show that under the changes of variable x =(Eq. 4.1) becomes:dxdr=1-x², x(0)=0.X =(Eq. 4.1)1/2x-A9*".v, T = (eg)²t, the IVP given byg1AB+1-x² 1-x 1+xUsing your answer to (d), solve the IVP (Eq. 4.2) and show that:1-e-2r1+e-²r.The IVP given by (Eq. 4.2) is of separable type. Briefly explain what this means(you do not need to solve the IVP at this stage).arks]Find A and B such that:=(Eq. 4.2)

Initial value problem: dvdt=g-εv2 , v0=0....[4.1] To Find: a) How does v vary with t. b) Show under…

The motion of an object falling from rest under gravity, subject to a drag force proportional to the square of the speed, may be modelled by the initial value problem (IVP): -=g-ev², v(0)=0. Here v is the speed of the object, t is time, g is gravitational acceleration (assumed constant) and is a constant. (a) Without solving the IVP, briefly describe how you expect v to vary with t. (b) (c) (d) (e) dv dt Show that under the changes of variable x = (Eq. 4.1) becomes: dx dr ==1-x², x(0)=0. 1 A B 1-x² 1-x 1+x 1/2 (9) v, t = (eg)¹²t, the IVP given by g X = (Eq. 4.1) The IVP given by (Eq. 4.2) is of separable type. Briefly explain what this means (you do not need to solve the IVP at this stage). arks] Find A and B such that: Using your answer to (d), solve the IVP (Eq. 4.2) and show that: 1-e-2r 1+e=2r (Eq. 4.2) AS

The motion of an object falling from rest under gravity, subject to a drag force proportional to the square of the speed, may be modelled by the initial value problem (IVP): -=g-ev², v(0)=0. Here v is the speed of the object, t is time, g is gravitational acceleration (assumed constant) and is a constant. (a) Without solving the IVP, briefly describe how you expect v to vary with t. (b) (c) (d) (e) dv dt Show that under the changes of variable x = (Eq. 4.1) becomes: dx dr ==1-x², x(0)=0. 1 A B 1-x² 1-x 1+x 1/2 (9) v, t = (eg)¹²t, the IVP given by g X = (Eq. 4.1) The IVP given by (Eq. 4.2) is of separable type. Briefly explain what this means (you do not need to solve the IVP at this stage). arks] Find A and B such that: Using your answer to (d), solve the IVP (Eq. 4.2) and show that: 1-e-2r 1+e=2r (Eq. 4.2) AS

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section3.5: Mathematical Modeling And Variation

Problem 7ECP: The kinetic energy E of an object varies jointly with the object’s mass m and the square of the...

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