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Knowing only the force is not sufficient to calculate the original height. This is because in order to find this, one needs to calculate the velocity or momentum of the object at the instant before it collides with the ground. Consider how the motion of the object is affected as it collides with the ground. As soon as the object makes contact, the force of ...

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Force alone will give you no information on the height the object fell from. Force is mass times acceleration, the latter is given by $g=9.81m/s^2$, which is (roughly) a constant on the earth's surface. It does not depend on the distance the object travelled before it hit the ground. The information you need is momentum, which contains the object's velocity. ...

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The equation comes from Newton's second law: $$F = ma$$ Galileo didn't know calculus (because Newton and Leibniz hadn't discovered it yet) so he couldn't derive the equation mathematically. Since we do know calculus we know that acceleration is the variation of velocity with time: $$a = \frac{dv}{dt}$$ And also the gravitational force $F$ is equal to ...

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The answer is a definite maybe! Ignoring air resistance the velocity a falling object hits the ground can be calculated using the appropriate SUVAT equation or by equating potential energy lost with kinetic energy gained. However this only tells you the speed the object hits the ground, and how hard it hits the ground depends on how fast it decelerates. If ...

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