KL UNIVERSITY: GUNTUR
Department of Mathematics A.Y. 2013-14
Home Assignment - I
Branch : CSE & ECM
Course: Mathematical Methods for Computing (11BS203)
Last date for submission: 30-08-2012 Course Coordinator : Dr. G. Suresh Kumar Max. Marks : 5
1. It is becoming increasingly common to use wind turbines to generate electric power. The
energy output of the power generated by a windmill depends upon the blade’s diameter
and velocity of the wind. A good estimate of the energy output is given by the following
formula:
EO = 0.01328 D2 V3,
where EO = Energy Output, D = Diameter of the windmill blade (m), V = Velocity of the wind in m/s.
Use Newton’s method to determine what should be the diameter of the windmill blade if one wishes to
generate 500 watts of electric power when the wind speed is 10mph. (five iterations and relative
approximate error after each iteration)
2. An electrical engineer supervises the production of three types of electrical components. Three kinds of
material- metal, plastic, and rubber are required for production. The amounts needed to produce each
component are
Component
Metal(g/component)
Plastic(g/component) Rubber(g/component)
1
1.5
0.30
0.20
2
1.0
0.80
0.50
3
0.5
0.40
1.0
If totals of 0.212, 0.095, and 0.106 kg of metal, plastic, and rubber, respectively, are
available each day, how many components can be produced per day? (hint: initial guess
80, 55, 60).
3. The speed of a train, running between two station is measured at different distances from the starting
station. If x is the distance in km from the starting station, then v(x) the speed (in km/hr) of the train at
the distance x is given by the following table:
x
0
50
100
150
200
250
v(x)
0
60
80
110
90
0
(i)
Find the approximate speed of the train at 25 km and 230 km.
(ii)
Find the approximate speed of the train at the mid point between the two stations, using Gauss
forward, Gauss backward, Stirling’s and Bessel’s interpolation formulas.
4. A slider in a machine move along a fixed straight rod. Its distance x cm along the rod is given below for
various values of the time t second. Find the velocity of the slider and its acceleration when t = 0.1 and
t = 0.6 seconds.
t
0
0.1
0.2
0.3
0.4
0.5
0.6
x
30.13
31.62
32.87
33.64
33.95
33.81
33.24
5. A rocket is launched from the ground. Its velocity is registered during the first 80 seconds and is given
in the table below. Find the distance moved by the rocket in 80 seconds and also the acceleration at t =
15 seconds.
t (sec)
0
10
20
30
40
50
60
70
80
v(m/sec)
30
31.63 33.34 35.47 37.75 40.33 43.25 46.69 50.67
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