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

The time taken to reach the maximum vertical height is given by the expression: [v = U+at]

v sinθ
0 = v sinθ − gt , rearranging for time t , we get: t =
g

Where, ‘t’ is the time taken to reach the highest point of the trajectory.

The time taken by the bullet to travel a vertical height of (h+h’) in the downward direction
after reaching the highest point is given by the expression:
1 1
2
2
s = Ut + at = 0 + gt , rearranging for time t , we get:
2 2
2 s 2 h + h
′
t = = - - - - (2.28)
g g

2
The distance (h’) could be computed using the expression: v = U + 2as
2
2
2
v sin θ
2
′
′
= v = 0 + 2ah′ , rearranging for height h , we get: h =
2g

Substituting the value of (h’) in equation (2.28) we get,

2 h + h 2h v sin θ
′
2
2
t = = +
g g 2g

The range ‘R’ of travel is given by:

Range R = horizontal component of velocity ∗ total time of travel

2
v sinθ 2h v sin θ
2
= R = v cos θ ∗ + +
g g 2g

Taking (v/g) common in the above equation, we get:

v 2 2hg
2
R = cos θ ∗ sinθ + + sin θ
g v 2
2hg
For ease of simplification, let us assume the expression 2 = k . Therefore, we have:
v

v 2
2
R = cos θ ∗ sinθ + k + sin θ
g

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