Max Impact of Free-Falling Bomb on Target

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SUMMARY

The discussion focuses on calculating the maximum impact of a free-falling bomb on a target while considering the sound produced by the bomb. The equations utilized include the free fall equation \(s = \frac{1}{2}gt^2\) and the sound travel equation \(s = ct\), where \(g\) is the acceleration due to gravity and \(c\) is the speed of sound at 340 m/s. The key conclusion is that the bomb must reach the target just as the sound of its fall arrives, ensuring that the sound reaches the target before the bomb does.

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Homework Statement


I have got a nice problem about free fall.
Consider a free-falling bomb vertically down at the target. The movement starts from rest. Bomb is giving sound - speed c= 340 m/s (from friction of air). What is the maximum impact of the bombs to her target (people) to hear sound alive ?


Homework Equations


I think I will use the equation of free fall and then the general equation for speed and acceleration.
s=1/2gt^2 (free fall)
s=ct (uniform motion sound)
v=gt (current speed uniformly accelerated motion)

The Attempt at a Solution


I think the basic premise is sound and that the bomb travels the same path:

1/2gt^2 = ct (calculate t)

Then t multiply the acceleration of gravity:

v= gt (and it is maximum velocity impact)

Of course it is, that the sound must be at the target faster (just) before the bomb.

It is right? Thanks very much (and sorry for my English).
 
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