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Document Title
Fundamentals of Stress and Vibration 2. Engineering Mechanics Chapter
[A Practical guide for aspiring Designers / Analysts]

Substituting the values of ‘L’, ‘V’ and ‘g’ in the above expression, we get:

1 10 ∗ (100) 2 80
−H = 100 tan θ − = H = −100 tan θ +
2
2
2
2 25 cos θ cos θ
Since, ‘H’ and ‘θ’ are variable, they must be plotted as dependent and independent variables
respectively. The zone for optimization is marked to select the optimum point, using the ranges for
‘H’ and ‘θ’ specified in the problem, as shown in [Fig 2.21].

[Fig 2.21: Minimum value of Height and Theta]

The minimum point is located in the area determined by the ranges of ‘H’ and ‘θ’. This is the
optimum value which minimizes (H).
The minimum value of ‘H’ could also be got more accurately via calculus, as follows:

80
We have, from equation . : H = −100 tan θ +
2
cos θ
Differentiating ‘H’ with respect to ‘θ’, we get:

dH
2
H = −100 tan θ + 80 cos −2 θ = = −100 sec θ + 80 ∗ −2 cos −3 θ ∗ (− sinθ)
dθ
dH 2 sinθ
2
= = −100 sec θ + 80 ∗
3
dθ cos θ

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 27 age 27
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