Dimensional Analysis and Unit ConversionsDate: 09/15/2002 at 19:47:25 From: Jenn Subject: Dimensional analysis Using dimensional analysis, convert 8 feet/second to kilometers/hour. I'm not sure how to work from hours to seconds. Here's what I tried, but the answer doesn't make sense to me. 8ft/sec (60s/1min)(60min/1hour)(1 yard/3ft)(1mile/1760yards) (1.609/1mile)=46339.2km/5280hours------8.78km/hours If you could please help, that would be wonderful. Thank you. Date: 09/16/2002 at 14:22:32 From: Doctor Ian Subject: Re: Dimensional analysis Hi Jenn, The only metric length conversion I have memorized is that 2.54 cm is _exactly_ one inch (it's how the inch is defined), so I like to use that: 8 ft 60 sec 60 min 12 in 2.54 cm 1 m 1 km ----- * ------ * ------ * ----- * ------- * ------ * ------- 1 sec 1 min 1 hr 1 ft 1 in 100 cm 1000 m 8 * 60 * 60 * 12 * 2.54 = ----------------------- 100 * 1000 = 8.78 km/hr which is the same thing you got. Actually, there are two other conversions that I've memorized, both of which come in quite handy: 60 mph is the same as 88 ft/sec. And there are about 8 kilometers in 5 miles. (The first is exact, the second is approximate.) So these can shorten the calculation a little: 60 mph 8 kilometers 8 ft/sec * --------- * ------------ 88 ft/sec 5 miles 8 * 60 * 8 = ---------- 88 * 5 60 * 8 = ------ 11 * 5 12 * 8 = ------ 11 = 8.72 km/hr This is less accurate, but it's easier, and in many situations it will be close enough. Note that we can use the 60/88 ratio to make a quick check of the result: 8 ft/sec is 1/11 of 88 ft/sec, so it's 1/11 of 60 mph, or a little less than 6 mph. So 8-point-something km/hr is at least in the right ballpark. The 8/5 ratio is handy when you see road signs with distances in kilometers instead of miles. (Some of these were put up during the 1980's, when there was some thought that the United States might switch to the metric system.) Does this help? - Doctor Ian, The Math Forum http://mathforum.org/dr.math/ |
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