(a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the quadcopter from its initial hovering point to the final resting point is described by: y = 2.15 + 2.09x – 0.41x²,0< x< 3.6 where x is the horizontal distance (in meters) from the point of release, and y is the total distance (in meters) from the initial point. (6) Estimate the travels distance of the quadcopter from the moment of its hovering point to the moment it rests, by using trapezoidal rule and appropriate Simpson's rule with h = 0.4 given that the arc length of the curve line is: L = dx Calculate the exact solution of the traveled distance by using a scientific calculator. (ii) (iii) Find the absolute error for cach methods (from Q2(a)(i)). (iv) Determine which method approximates better.
(a) A miniature quadcopter flies in a curve line from one point to another. Suppose that the path of the quadcopter from its initial hovering point to the final resting point is described by: y = 2.15 + 2.09x – 0.41x²,0< x< 3.6 where x is the horizontal distance (in meters) from the point of release, and y is the total distance (in meters) from the initial point. (6) Estimate the travels distance of the quadcopter from the moment of its hovering point to the moment it rests, by using trapezoidal rule and appropriate Simpson's rule with h = 0.4 given that the arc length of the curve line is: L = dx Calculate the exact solution of the traveled distance by using a scientific calculator. (ii) (iii) Find the absolute error for cach methods (from Q2(a)(i)). (iv) Determine which method approximates better.
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:A miniature quadcopter flies in a curve line from one point to another. Suppose that
the path of the quadcopter from its initial hovering point to the final resting point is
described by:
Q2
(a)
y = 2.15 + 2.09x - 0.41x?,0 s xs 3.6
where x is the horizontal distance (in meters) from the point of release, and y is the
total distance (in meters) from the initial point.
Estimate the travels distance of the quadcopter from the moment of its
hovering point to the moment it rests, by using trapezoidal rule and
appropriate Simpson's rule with h = 0.4 given that the arc length of the
curve line is:
(i)
2
L =
1+
dx
(ii)
Calculate the exact solution of the traveled distance by using a scientific
calculator.
Find the absolute error for each methods (from Q2(a)(i)).
(iv)
Determine which method approximates better.
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