College Physics....please help and explain.?

Question

Sand dunes on a desert island move as sand is swept up the windward side to settle in the leeward side. Such "walking" dunes have been known to travel 23 feet in a year and can travel as much as 90 feet per year in particularly windy times. Calculate the average speed in each case in m/s.

23 ft/y = ____m/s

90 ft/y = ____m/s

(b) Fingernails grow at the rate of drifting continents, about 10 mm/yr. Approximately how long did it take for North America to separate from Europe, a distance of about 3000 mi?

____y

Thanks for any help!

Answer 1

These are just unit conversions.  Find out how many feet are in a meter.  23 ft / (however many ft/m) will give you how many meters a year the dune moves. Then, divide that by the number of seconds in a year.  Voila, m/s.  It will be a very small number.

B) Same story.  Convert miles to mm, then divide by 10 to figure out how many years it took (this will be a large number).  You can find conversion factors on Google, heck, it might even do it for you.

Answer 2

Make it a practice of using dimensional analysis for solving problems. You will find it a very useful tool for determining units, and checking the result of an equation.

For the first conversion,

You have: ft/y

You want: m/s

x ft/yr * 1 yr/365 days * 1 day/24 hr * 1 hr/3600 s = y ft/s

y ft/s * 12 in/ft * 2.54 cm/in * 1 m/100 cm = z m/s

Notice how a unit in the denominator of each conversion factor cancels a unit in the numerator until what is left is the unit you want.

What you are effectively doing is multiplying by 1 in each step, so you are not changing the value, just the unit. This works for all equations.

Here's a handy link about dimensional analysis with a lot of examples:

http://alysion.org/dimensional/fun.htm

Here's a link to an on-line conversion calculator:

http://www.onlineconversion.com/