Page 105 - MATLAB an introduction with applications

90 ——— MATLAB: An Introduction with Applications

Considering the airplane with a velocity of 500km/h opens its parachute and starts decelerating at
t = 0 second, write a MATLAB program to solve the differential equation and plot the velocity from
t = 0 second until the airplane stops.
P1.30: Obtain the first and second derivatives of the following functions using MATLAB’s symbolic
mathematics.
4
5
(a) F(x) = x – 8x + 5x – 7x + 11x – 9
2
3
2
3
(b) F(x) = (x + 3x – 8)(x + 21)
3
2
(c) F(x) = (3x – 8x + 5x + 9)/(x + 2)
2
5
3
4
(d) F(x) = (x – 3x + 5x + 8x – 13) 2
3
6
7
2
(e) F(x) = (x + 8x –11)/(x – 7x + 5x + 9x – 17)
P1.31: Determine the values of the following integrals using MATLAB’s symbolic functions.
7 5 3 2
(a) 5x x 3x 8x 7 dx
(b) x cos x
2
(c) x 2/3 sin 2x
1.8
(d) 0.2 x 2 sin x dx
0.2 xdx
(e) 1
5 1
P1.32: Use MATLAB to calculate the following integral: 2 dx
0 0.8x 0.5x 2
10
P1.33: Use MATLAB to calculate the following integral: ∫ cos (0.5 )sin (0.5 )dx
2
4
x
x
0
P1.34: The variation of gravitational acceleration g with altitude y is given by:
R 2
g = g o ,
(R ) y 2
2
where R = 6371 km is radius of the earth and g = 9.81 m/s is gravitational acceleration at sea level.
o
The change in the gravitational potential energy ∆U of an object that is raised up from the earth is given by:
y
∫
∆U = mgdy
0

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