Aim #7: How do we convert from one unit of measure to another? Homework: Handout Do Now: If a car uses 18 gallons of gas to travel 558 miles, then how far can the car travel on 12 gallons of gas?
Dimensional Analysis is a method for unit conversion -A ratio is a comparison of two numbers by division. If two numbers represent quantities measured in different units, then the ratio is a rate. -A unit rate is a rate with a denominator of 1. -To change from one unit of measure to another, we can use rates that equal 1.
Dimensional analysis is done as follows: * Determine the units given and desired. * Find the necessary conversion factor(s). * Write a conversion ratio in order to cancel out undesired units and retain desired units. * Set up an expression using multiplication and conversion ratio. Conversion expression will ultimately convert to units desired through multiplication and cross simplification.
Ex. A driveway is feet long. How long is this in inches? (12 inches = 1 foot) Perform each of the following conversions by showing all work. 1) 30 km/hr to m/min
2) 800 m/min to km/hr
3) 30 m/min to cm/sec
4) 70 cm/sec to m/min 1) A mourning dove can reach 35 miles per hour. How fast is that in feet per hour?
2) A cheetah ran 300 feet in 2.92 seconds. What was the cheetah's average speed in miles per minute? Round to the nearest hundredth.
3) A car website advertises that a new car averages 15 km/liter of gas. What is the equivalent gas usage in miles per gallon? Round to the nearest whole number.
4) A worm moves 8 inches in 5 seconds. How many miles per hour is this? Round to the nearest hundredth.
5) Traveling 50 miles per hour is the same as how many feet per second? 6) Sally Leadfoot was pulled over on her way from Syracuse to Ithaca by an officer claiming she was speeding. The speed limit is 65 mi/hr and Sally had traveled 97 km in 102 minutes. How fast was Sally‛s average speed? Round to the nearest whole number. Does she deserve a ticket?
7) Jen took 14.5 seconds to run the 100-meter dash. Calculate the time in meters per minute. Round to the nearest thousandth.
8) Dan wants to convert 800 m/min to km/hr, as shown below. Which ratio is incorrectly written to covert his speed?
Let's sum it up! * Write the conversion as a fraction equivalent to 1 * Multiply * Cancel any units that are the same in the numerator as the denominator. (Remember: If you want only one unit to remain make sure it is in numerator.) Attachments
ANGLE OF ELEVATION AND ANGLE OF DEPRESSION.gsp