dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter1: Equations And Graphs
Section1.3: Lines
Problem 92E
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MATH 252 – TRACTRIX
1) Suppose that you are holding a rope of length a and you are going to walk and drag an object
behind you.
In particular suppose that your initial position is (0,0) and that the object's initial position is
(a, 0) and that you will walk in the direction of the positive y-axis.
We wish to find an equation for the path of the dragged object. Let's only worry about the
upper portion (matching walking in positive y direction)
Tractrix with object initially at b
(4,0)
YOU DO: Suppose the object is at (x, y). Determine the y - coordinate of the puller.
HINT: Set up a right triangle. You know 2 of its measurements.
The pulled object is always going towards the puller. We need that following the slope of the
curve would result in the object meeting the current position of the puller. We also have an
initial condition that y(a)
= 0. These conditions give us a differential equation:
dy
Va²-x²
with initial condition y(a) = 0.
dx
Va2-t2
dt
This can be solved by y =
Transcribed Image Text:MATH 252 – TRACTRIX 1) Suppose that you are holding a rope of length a and you are going to walk and drag an object behind you. In particular suppose that your initial position is (0,0) and that the object's initial position is (a, 0) and that you will walk in the direction of the positive y-axis. We wish to find an equation for the path of the dragged object. Let's only worry about the upper portion (matching walking in positive y direction) Tractrix with object initially at b (4,0) YOU DO: Suppose the object is at (x, y). Determine the y - coordinate of the puller. HINT: Set up a right triangle. You know 2 of its measurements. The pulled object is always going towards the puller. We need that following the slope of the curve would result in the object meeting the current position of the puller. We also have an initial condition that y(a) = 0. These conditions give us a differential equation: dy Va²-x² with initial condition y(a) = 0. dx Va2-t2 dt This can be solved by y =
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