I think you DO lose something if you don't calculate numerical answers at intermediate steps, namely, do my answer make sense at this point in the reasoning?
Yes, you can calculate the range of a horizontal projectile by deriving the range equation and plugging in values for the angle and initial velocity. But I prefer calculate the initial velocity in the x direction and y direction given the velocity and angle. Does that make sense? If the angle's 45 degrees both x and y should be about 2/3 of the total, and if you don't get that your calculator may be set on radian measure. Then calculate the time in the air given the y velocity. Does that make sense? If you get a time in the air of 1000 seconds for a 5 m/s initial velocity it probably doesn't. Then calculate the distance traveled using the x velocity and the time in the air. Does that make sense? If you get a range of 2 cm and you're initial x velocity is 3.5 m/s and your time is 2 s it probably doesn't. Now one thing you could do that would drive 'em nuts is solve the problem algebraically as suggested, but do these little numerical checks in the margins in SI. Nat From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Bill Hooper Sent: Monday, 2007 December 03 14:54 To: U.S. Metric Association Subject: [USMA:39842] Re: the U.S. SHALL go metric On 2007 Dec 3 , at 11:26 AM, Mike Millet wrote: ... I'm struggling in the class because there is no consistency between problems, they all use different measurements, ... Math is difficult enough that I think it's doing a disservice to people to make it unnecessarily harder by flipping units around. The math is not difficult; just the unit conversions are. There's a way around it, some of it anyway. Solve the problems entirely algebraically. That way, you don't need to enter ANY units and as a matter of fact you don't have to enter any numbers either. At the end, there will be only two steps left to do; plug in the values (simple substitution) and do the arithmetic. You can and should, really, substitute the values in the given units even if they are not coherent in order to demonstrate that you know which values are represented by which algebraic symbols but carrying out the arithmetic will not give the right answer until the units are in a coherent set. At that penultimate point, you have done all the really important science and engineering of the problem and that there are only two relatively unimportant steps to go: (1) converting the given values to a coherent set of units (SI metric being best) and (2) carrying out the trivial step of doing the arithmetic on your calculator, You should persuade the professor that leaving out those two minor steps should not cost you more than a point or two out of the whole problem. That gives you time to work on the important aspects of the other problems on the test at the cost of a mere point or two on the first problem. Losing no more than a point or two here and there should still allow you to get an A on the test. If you have time at the end of the test, when you have zipped through all the other problems by this simplified method, you could go back and try to recoup the couple points initially lost by not completing the trivial unit conversions and calculator arithmetic. I suggest this to you as a student but I also suggest it to any of you who are or may become teachers. It is the way I taught my physics courses (algebraic based and calculus based). Of course I never gave them values in Ye Olde English units. (Oh, OK! Yes I did before 1975.) But I did tell my students that plugging in the numbers and doing the arithmetic were trivial parts of any problem and that I would never take off more than 1 point for failing to carry out the arithmetic or doing it incorrectly. (I did insist that they plug in the numbers just to show me that they knew what went where.) I even went so far as to suggest that sometime I might give a test on which the directions would tell them to carry out the entire problem without substituting any values until the last step AND that after the substitutions were made, I would REQUIRE that they NOT carry out the arithmetic. I would DEDUCT points if they did carry out the arithmetic which meant that I would deduct points even for the right answer. I never actually gave such a test, but I regret that I did not. I should have done so at least once so I could say that I did it. Throughout all this, my mantra was: "Answers don't count, METHODS do. Yesterday's answers may not be correct in tomorrow's world, but today's methods will still work tomorrow to solve tomorrow's problems." Of course, the purpose of learning the methods in the academic world is to prepare you to find the FINAL answers in the real world. However, that final step of doing the unit conversion (if necessary) and arithmetic are things that can be turned over to junior staff members and their calculators. We must learn to do that, too, but it is a relatively routine thing to learn to do. The real science and engineering, however, comes before that. Regards, Bill Hooper Fernandina Beach, Florida, USA ========================== Make It Simple; Make It Metric! ==========================
