4. The velocity of a body moving through a resisting medium with resistance proportional to the square of the velocity can be modelled by the differential equation i) dv -0.003 v², v(0) = vo. dt By separating the variables show that the velocity is given by v(t) Vo 1 +0.003 vot On a still day a small hovercraft is moving at 6m/s when its fan suddenly fails. The motion of the hovercraft thereafter can be modelled using the differential equation above. Taking vo = 6 find the hovercraft's velocity four seconds later.

4. The velocity of a body moving through a resisting medium with resistance proportional to the square of the velocity can be modelled by the differential equation i) dv -0.003 v², v(0) = vo. dt By separating the variables show that the velocity is given by v(t) Vo 1 +0.003 vot On a still day a small hovercraft is moving at 6m/s when its fan suddenly fails. The motion of the hovercraft thereafter can be modelled using the differential equation above. Taking vo = 6 find the hovercraft's velocity four seconds later.

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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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Concept explainers

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.

Topic Video

Question

Please answer very soon will give rating surely

4. The velocity of a body moving through a resisting medium with resistance proportional to the
square of the velocity can be modelled by the differential equation
dv
-0.003 v?, v(0) = vo.
dt
i)
By separating the variables show that the velocity is given by
vo
v(t):
1+ 0.003 vot '
On a still day a small hovercraft is moving at 6m/s when its fan suddenly fails. The
motion of the hovercraft thereafter can be modelled using the differential equation
above. Taking vo = 6 find the hovercraft's velocity four seconds later.
111)
With vo = 6 complete the application of one step of the modified Euler method
(given below) with a step-length of h = 4 to approximate the solution to the
differential equation at t = 4s. Compare the approximation you obtain with the exact
value from part ii).
Modified Euler method:
k1 = hf (vo)
k2 = hf(vo + k1)
vi = vo +;(k1 + k2).

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