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Imagine that you had to solve a novel physics problem today, either in real life or on a test, and that you had a physics text that contained the relevant physics as well as a selection of solved problems. Even if you had a search engine to aid your retrieval of this material, would you feel confident that you could solve your problem?
Probably you’d not you wouldn't feel confident if your problem differed in any significant respect from all of the ones in your collection, or if you had to recognize this feature in the real world. For example, you might have the equation for the range of a projectile fired at a certain speed and angle above horizontal. But your problem might be to shoot at enemies attacking from 100 meters beyond your troops who were dug in under some tall trees. In this case you'd need to be able to calculate whether the explosive projectiles would clear the trees on their way to the target, and if not how much slower than usual they must be fired so that they would. In order to solve this problem, or even to recognize that it was a problem, you’d have to visualize the situation and understand how the range formula is obtained. If you understand that the horizontal and vertical components of the motion are independent, you'd find the time when the projectile will would be over your troops from its horizontal equation of motion, then find its height from the vertical equation of motion, then adjust the muzzle velocity to avoid the trees. (The failure to recognize and solve this problem cost the US several fatalities in Vietnam – see Friendly Fire by C. D. B. Bryan.)
Please take a moment to reflect on what you have been trained to do when you study physics or review your physics homework. Very likely it is to memorize the formulae in the textbook and the solutions to the problems you’ve done. But the above example should show you that this is not sufficient – somehow you need to understand the material as well. Understanding involves being able to visualize the problem and to see the deep regularities (e.g. conservation of energy) that underlie the solution to many of these example problems. Paradoxically, if your understanding is at this level, you only need to remember the typical schema (plan of attack) involving that each concept in order to be able to solve many problems – you don’t need to know the detailed solution of many different example problems involving that concept.
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