hw1_solutions

# hw1_solutions - Homework#1 Solutions Astro 10 spring 2010...

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Homework #1: Solutions Astro 10, spring 2010 General Notes to Graders: If numerical answers are roughly correct, do not take marks off. Award part marks if the student has made some progress with the question. 1. [5 points] This is a straight forward unit conversion problem, but things will get messy and complicated if you are careless with units . So, let’s do things nice and slow (of course, you can do the following steps in any order - this is just a suggestion). First convert miles into inches, making sure your units cancel properly. 70 miles hour = (70 miles hour )( 5280 feet 1 mile )( 12 inches 1 foot ) = 4435200 inches hour Now convert hours into seconds, making sure your units will cancel properly. 4435200 inches hour = (4435200 inches hour )( 1 hour 60 minutes )( 1 minute 60 seconds ) = 1232 inches second Now convert inches to cm. 1232 inches second = (1232 inches second )( 2 . 54 cm 1 inch ) = 3129 . 28 cm second Finally, convert cm to m. 3129 . 28 cm second = (3129 . 28 cm second )( 1 m 100 cm ) = 31 . 3 m second Notes to graders: 1 point off if correct but careless with units. 2 points off if correct but did not use 1 inch = 2.54 cm conversion rule as instructed. 2. [5 points] This simple problem can be solved a variety of ways, but I want you to do this with a ratio. It’s good practice for later on in the course. Assume there is some relationship between speed ( v ) and time it takes to travel ( t ), such that the faster the speed, the smaller the travel time. This is written as v 1 /t . When you compare two different speeds as a ratio, it doesn’t matter what the constant of proportionality is since they will cancel. Let v 1 be the speed of light ( 3 x 10 8 m/s), and t 1 be 8.3 minutes. Let v 2 be the speed of the airplane (340 m/s) and t 2 the unknown time. The reason we can express the following as a ratio is that the distance is the same (and thus will cancel). Therefore: t 2 t 1 = v 1 v 2 t 2 = ( 3 x 10 8 m/s 340 m/s )(8 . 3 minutes ) t 2 = 7 . 3 x 10 6 minutes = 13 . 9 years 1

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Notes to graders: 1 point off if correct but careless with units. 1 point off if correct but did not
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