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An object of a given mass falls from an unknown height. If the force exerted by the object on contact with the ground is known, how would you ascertain the height from which the object fell?

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closed as off-topic by Olin Lathrop, Dilaton, Kyle Kanos, Abhimanyu Pallavi Sudhir, ja72 Mar 7 '14 at 17:59

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    $\begingroup$ What do you think, and why? (I resisted the impulse to answer with a single short word :-) ) $\endgroup$ – Carl Witthoft Feb 27 '14 at 18:19
  • $\begingroup$ Hi A A. Welcome to Phys.SE. If you haven't already done so, please take a minute to read the definition of when to use the homework tag, and the Phys.SE policy for homework-like problems. $\endgroup$ – Qmechanic Mar 1 '14 at 13:37
  • $\begingroup$ Hi A A, concerning your request to delete your own question, note that it is possible to do that yourself. $\endgroup$ – Qmechanic Mar 2 '14 at 16:49
  • $\begingroup$ It is sometimes possible to delete your own questions, but not in this case because there is an upvoted answer. However, the moderators will not help you subvert that limitation. $\endgroup$ – dmckee Mar 2 '14 at 17:00
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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 you can measure the force as a function of time during the collision you can calculate the total impulse, and since this is equal to the momentum change you can calculate the original momentum and hence the original velocity. Just calculating the peak force doesn't help because it could be a hard slow moving object decelerating suddenly or a soft fast moving object decelerating slowly.

I haven't gone into specifics, since this looks rather like a homework question, but this should direct you to the physics you need to answer your problem.

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