Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 13 seconds later, the boat has slowed to 16 ft/s. Assume that the resistance it encounters while coasting is proportional to its velocity, v. That is, How far will the boat coast in all? dv dt = -k v help (formulas) Solve the problem by following the steps outlined below. The above differential equation has general solution (use C for the arbitrary constant if necessary): v(t) = Cekt ft/s help (formulas) Use the initial conditions v(0) and v(13) to find the constant C and the drag coefficient k. C = 40 and k = = 0.0705 help (numbers) Find the velocity function of the motorboat. v(t) = ft/s help (formulas) Find the position function, x(t), of the motorboat. Assume x (0) = 0. x(t) == 567.3759 (1-e-0.0705t) ft help (formulas) Find the limit of x(t) as t approaches ∞ (this is how far the boat will coast). lim x(t) = ft help (numbers) t→∞
Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 13 seconds later, the boat has slowed to 16 ft/s. Assume that the resistance it encounters while coasting is proportional to its velocity, v. That is, How far will the boat coast in all? dv dt = -k v help (formulas) Solve the problem by following the steps outlined below. The above differential equation has general solution (use C for the arbitrary constant if necessary): v(t) = Cekt ft/s help (formulas) Use the initial conditions v(0) and v(13) to find the constant C and the drag coefficient k. C = 40 and k = = 0.0705 help (numbers) Find the velocity function of the motorboat. v(t) = ft/s help (formulas) Find the position function, x(t), of the motorboat. Assume x (0) = 0. x(t) == 567.3759 (1-e-0.0705t) ft help (formulas) Find the limit of x(t) as t approaches ∞ (this is how far the boat will coast). lim x(t) = ft help (numbers) t→∞
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:Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 13 seconds later, the boat has slowed to 16 ft/s. Assume that
the resistance it encounters while coasting is proportional to its velocity, v. That is,
How far will the boat coast in all?
dv
dt
=
-k v help (formulas)
Solve the problem by following the steps outlined below.
The above differential equation has general solution (use C for the arbitrary constant if necessary):
v(t) = Cekt ft/s help (formulas)
Use the initial conditions v(0) and v(13) to find the constant C and the drag coefficient k.
C
= 40 and k =
=
0.0705 help (numbers)
Find the velocity function of the motorboat.
v(t)
=
ft/s help (formulas)
Find the position function, x(t), of the motorboat. Assume x (0) = 0.
x(t)
==
567.3759 (1-e-0.0705t) ft help (formulas)
Find the limit of x(t) as t approaches ∞ (this is how far the boat will coast).
lim x(t)
=
ft help (numbers)
t→∞
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