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

From [Fig 2.21], it can be seen that, the slope of the curve is zero at minimum ‘H’, therefore, we
have:

2 sinθ 100 sin θ 5
2
0 = −100 sec θ + 80 ∗ = = 160 = = tan θ
2
3
3
cos θ cos θ cos θ 8
Therefore, we have θ = 32.005
0
It can be observed that the value of ‘θ’ for minimum ‘H’ via XLS, as shown in [Fig 2.21], is close to
the exact value.
L 100
The time of flight for equation . is: t = = = 4.72 s
V cos θ 25 cos 32.005

It can be shown that, the range of 100 m (given) is maximum for the computed ‘H’ and ‘θ’.

Example 5: For (Example 4) establish a general expression for maximum range (R) of the
projectile.

Solution 5: For the given situation, the following example computes the expression for
maximum range:

The canon is at a height ‘h’ from the ground. The bullet traces a parabolic path, reaching a
maximum height of (h+h’) from the ground. The total time the bullet takes to reach the ground,
which is the range of travel for the bullet, is a summation of the time taken by the bullet to reach
the maximum height (h+h’) and the time to reach the target, as shown in [Fig 2.22].

[Fig 2.22: Canon firing at the target]

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