Consider the differential equation describing a falling object where the drag force is proportional to velocity, assuming velocity is positive in the upward direction: me' mg – kv Let m be the mass of the object, g be the acceleration due to gravity, and k > 0 the constant of proportionality. (a) Find all equilibrium solutions of the differential equation. What is the physical meaning of this solution? (b) Suppose the initial velocity is vo, so the initial condition becomes v(0) = vo. Solve the IVP for v(t). (c) Suppose a rock weighing 3.5 lbs is thrown down from 25 feet above the ground with an initial velocity of -2 ft/s Let k = 1/32 and assume that the drag force is proportional to velocity. Find an equation describing the position.
Consider the differential equation describing a falling object where the drag force is proportional to velocity, assuming velocity is positive in the upward direction: me' mg – kv Let m be the mass of the object, g be the acceleration due to gravity, and k > 0 the constant of proportionality. (a) Find all equilibrium solutions of the differential equation. What is the physical meaning of this solution? (b) Suppose the initial velocity is vo, so the initial condition becomes v(0) = vo. Solve the IVP for v(t). (c) Suppose a rock weighing 3.5 lbs is thrown down from 25 feet above the ground with an initial velocity of -2 ft/s Let k = 1/32 and assume that the drag force is proportional to velocity. Find an equation describing the position.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider the differential equation describing a falling object where the drag force is proportional to velocity, assuming
velocity is positive in the upward direction:
mu' = -mg – kv
Let m be the mass of the object, g be the acceleration due to gravity, and k > () the constant of proportionality.
(a) Find all equilibrium solutions of the differential equation. What is the physical meaning of this solution?
(b) Suppose the initial velocity is vo, so the initial condition becomes v(0) = vg. Solve the IVP for v(t).
(c) Suppose a rock weighing 3.5 lbs is thrown down from 25 fect above the ground with an initial velocity of -2 ft/s.
Let k = 1/32 and assume that the drag force is proportional to velocity. Find an equation describing the position,
y(t), of the rock.
Hint: You can use your solution from part (b). Use g = 32 ft/s² and recall that weight = mass · g.
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