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

[Fig 2.19: Canon firing at the target]

‘Ž—–‹‘ǣ •‹ ‡ –Š‡ ƒ‘ ‹• ϐ‹”‡† ƒ– ƒ ƒ‰Ž‡ ȋɅȌǡ Š‘”‹œ‘–ƒŽ ƒ† ˜‡”–‹ ƒŽ ‘’‘‡–• ‘ˆ ˜‡Ž‘ ‹–›
ȋ Ȍ ‡š‹•–ǡ ƒ• •Š‘™ ‹ ȏ ‹‰ ʹǤʹͲȐǤ

[Fig 2.20: components of velocity]

The horizontal displacement (L) of the bullet is given by: [L = V cos θ ∗ time of flight t - - - - (2.25)

The vertical displacement (H) is negative, as the target is H meters below the point of fire. Further,
the initial velocity is vertically upwards and the acceleration due to gravity for an upward motion is
negative.

1 1
2
2
Using the expression: s = Ut + at , we get: −H = V sinθ t − gt - - - - (2.26)
2 2
Substituting the value of ‘t’ from equation (2.25) in equation (2.26), we get:
L 1 L 2 1 gL 2
−H = V sin θ − g = −H = L tan θ −
2
2
V cos θ 2 V cos θ 2 V cos θ

Page 26 QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries,