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

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Linear quantities Angular quantities

2
2
V = u + 2as Ω = ω + 2αθ
2
2
V = u + at Ω = ω + at

1 1
2
s = ut + at θ = ωt + αt
2
2 2
Where,

V Final velocity Ω Final angular velocity

u Initial velocity ω Initial Angular velocity

a Acceleration α Angular acceleration

t Time θ Angular displacement

s Displacement

Example 4 (Basic Optimization): Consider a cannon firing a ball, as shown in [Fig 2.19].
What is the optimum angle θ and height (H), with which, the ball must be fired such that it hits
the target?
Parameters of the problem are as tabulated.

Parameters Magnitude

Velocity of fire (V) 25 m/s

Limits of variable height (H) 40m to 80m

Limits of angle of projection (θ) 30° to 40°

Horizontal displacement of bullet (L) 100 m

Acceleration due to gravity (g) 10 m/s
2
0
The accuracy of angle in the final solution must be within ±0.1 .

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, P
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Copyright Diary No – 9119/2018-CO/L